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Topics referred to by the same term
In mathematics, Naimark theorem may refer to: Gelfand–Naimark theorem Naimark's dilation theorem This disambiguation page lists mathematics articles associated
Naimark_theorem
Mathematics theorem in functional analysis
In mathematics, the Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-subalgebra of bounded operators
Gelfand–Naimark_theorem
operator theory, Naimark's dilation theorem is a result that characterizes positive operator valued measures. It is named after Mark Naimark from his 1943
Naimark's_dilation_theorem
Soviet mathematician (1909–1978)
written in Russian) Naimark's problem Naimark's dilation theorem GNS theorem Gelfand–Naimark theorem Naimark equivalence "Naimark biography". MacTutor
Mark_Naimark
Correspondence in functional analysis
a C ∗ {\displaystyle C^{*}} -algebra A {\displaystyle A} , the Gelfand–Naimark–Segal construction establishes a correspondence between cyclic ∗ {\displaystyle
Gelfand–Naimark–Segal construction
Gelfand–Naimark–Segal_construction
Mathematical representation in functional analysis
of an integrable function. In the latter case, the Gelfand–Naimark representation theorem is one avenue in the development of spectral theory for normal
Gelfand_representation
Proof that every structure with certain properties is isomorphic to another structure
The Gelfand representation (also known as the commutative Gelfand–Naimark theorem) states that any commutative C*-algebra is isomorphic to an algebra
Representation_theorem
Surname list
question in the field of functional analysis Naimark's dilation theorem Gelfand–Naimark theorem Gelfand–Naimark–Segal construction Neumark (surname) This
Naimark
theorem (functional analysis) Gelfand–Mazur theorem (Banach algebra) Gelfand–Naimark theorem (functional analysis) Hardy–Littlewood maximal theorem (real
List_of_theorems
Topological complex vector space
for a suitable Hilbert space, H; this is the content of the Gelfand–Naimark theorem. Let H be a separable infinite-dimensional Hilbert space. The algebra
C*-algebra
Duality between a group and its representations
endomorphisms of the monoidal unit contains only scalars. Gelfand–Naimark theorem Doplicher, S.; Roberts, J. (1989). "A new duality theory for compact
Tannaka–Krein_duality
Mathematical set with some added structure
the operations of pointwise addition and multiplication. The Gelfand–Naimark theorem implied that there is a correspondence between commutative C*-algebras
Space_(mathematics)
Theorem
consequences of Stinespring's theorem. Historically, some of the results below preceded Stinespring's theorem. The Gelfand–Naimark–Segal (GNS) construction
Stinespring_dilation_theorem
his theorem of extreme points that entered all text books in functional analysis, as Krein-Milman theorem Mark Naimark, author of the Gelfand–Naimark theorem
List of Russian mathematicians
List_of_Russian_mathematicians
Soviet mathematician (1913–2009)
algebra theory; the Gelfand–Mazur theorem in Banach algebra theory; the Gelfand–Naimark theorem; the Gelfand–Naimark–Segal construction; Gelfand–Shilov
Israel_Gelfand
Mathematical ring whose elements are matrices
If A is non-unital, then Mn(A) is also non-unital. By the Gelfand–Naimark theorem, there exists a Hilbert space H and an isometric *-isomorphism from
Matrix_ring
Concept in mathematics
geometry, the quantum groups. This dual can be shown, by the Gelfand–Naimark theorem, to contain the C* algebra of the corresponding Lie group. This relationship
Universal_enveloping_algebra
Generalized measurement in quantum mechanics
space. Note: An alternate spelling of this is "Neumark's Theorem" Naimark's dilation theorem shows how POVMs can be obtained from PVMs acting on a larger
POVM
Branch of mathematics
noncommutative topological spaces. This terminology is motivated by the Gelfand–Naimark theorem, which identifies commutative C*-algebras with algebras of continuous
Noncommutative_geometry
Gelfand–Naimark theorem Gelfand–Naimark–Segal construction Von Neumann algebra Abelian von Neumann algebra von Neumann double commutant theorem Commutant
List of functional analysis topics
List_of_functional_analysis_topics
and C*-algebraic concepts. The term has its origins in the Gelfand–Naimark theorem, which implies the duality of the category of locally compact Hausdorff
Noncommutative_topology
Normed vector space that is complete
{\displaystyle H} is a fundamental example of C*-algebra. The Gelfand–Naimark theorem states that every C*-algebra is isometrically isomorphic to a C*-subalgebra
Banach_space
{\mathsf {ZFC}}} Gelfand–Naimark theorem Akemann, Charles; Weaver, Nik (2004), "Consistency of a counterexample to Naimark's problem", Proceedings of
Naimark's_problem
Function acting on the space of physical states in physics
importance in itself. For further information, see C*-algebra and Gelfand–Naimark theorem. The mathematical formulation of quantum mechanics (QM) is built upon
Operator_(physics)
Surjective bounded operator on a Hilbert space preserving the inner product
Belfi, Victor A. (1986). Characterizations of C*-Algebras: The Gelfand-Naimark Theorems. New York: Marcel Dekker. ISBN 0-8247-7569-4. Halmos, Paul (1982).
Unitary_operator
Structure in Ring Theory (Mathematics)
Jacobson radical of a C*-algebra is {0}. This follows from the Gelfand–Naimark theorem and the fact that for a C*-algebra, a topologically irreducible *-representation
Jacobson_radical
Topics referred to by the same term
theorem may refer to: Dilation theorem for contraction semigroups Sz.-Nagy's dilation theorem Stinespring dilation theorem Naimark's dilation theorem
Dilation_theorem
Surname list
complex-valued functions the Gelfand–Naimark–Segal construction the Gelfand–Naimark theorem the Gelfand–Mazur theorem a Gelfand pair, a pair (G,K) consisting
Gelfand
Representation theory
historical notes on the Plancherel theorem for spherical functions Harish-Chandra 1951 Harish-Chandra 1952 Gelfand & Naimark 1948 Guillemin & Sternberg 1977
Plancherel theorem for spherical functions
Plancherel_theorem_for_spherical_functions
coined the term Informatics Mark Naimark, author of the Gelfand–Naimark theorem and Naimark's problem Pyotr Novikov, solved the word problem for groups and
List_of_Russian_scientists
G/K).} Since A(K\G/K) is a commutative C* algebra, by the Gelfand–Naimark theorem it has the form C0(X), where X is the locally compact space of norm
Zonal_spherical_function
Victor A. Belfi (1986). Characterizations of C*-Algebras: The Gelfand–Naimark Theorems. New York: Marcel Dekker. ISBN 0-8247-7569-4. Russo, B.; H. A. Dye
Russo–Dye_theorem
by the σt(ar)'s. It is commutative and separable so, by the Gelfand–Naimark theorem, can be identified with C(Z) where Z is its spectrum, a compact metric
Ergodic_flow
continuous functions, which determine the group completely. Gelfand–Naimark theorem Representation theory И. М. Гельфанд, Д. А. Райков, Неприводимые унитарные
Gelfand–Raikov_theorem
Soviet mathematician (1907–1989)
Whitney), but was not allowed to attend the ceremony. David Milman, Mark Naimark, Israel Gohberg, Vadym Adamyan, Mikhail Livsic and other known mathematicians
Mark_Krein
Mathematical category formed by reversing morphisms
opposite of the category of (discrete) abelian groups. By the Gelfand–Naimark theorem, the category of localizable measurable spaces (with measurable maps)
Opposite_category
American mathematician
C*-algebra. This work was motivated in part by the classical Gelfand–Naimark theorem for C*-algebras and by the work of M. Takesaki and J. Tomiyama. Doran
Robert_S._Doran
M(A) is Cb(X), the continuous bounded functions on X. By the Gelfand–Naimark theorem, one has the isomorphism of C*-algebras C b ( X ) ≃ C ( Y ) {\displaystyle
Multiplier_algebra
History of maths
coefficients. 1943 Israel Gelfand–Mark Naimark Gelfand–Naimark theorem (sometimes called Gelfand isomorphism theorem): The category Haus of locally compact
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
{\displaystyle PU^{n}P=T^{n}} . This is precisely Sz.-Nagy's dilation theorem and hints at an important dilation-theoretic characterization of positivity
Positive-definite function on a group
Positive-definite_function_on_a_group
Type of vector space in math
now known as von Neumann algebras. In the 1940s, Israel Gelfand, Mark Naimark and Irving Segal gave a definition of a kind of operator algebras called
Hilbert_space
Mathematical method in functional analysis
so that H is constructed from ϕ {\displaystyle \phi } using the Gelfand–Naimark–Segal construction. Since Ω is separating, ϕ {\displaystyle \phi } is faithful
Tomita–Takesaki_theory
Unitary representations of a Lie group
unitary representations of the Lie group SL(2, R) are due to Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952). We choose a basis
Representation theory of SL2(R)
Representation_theory_of_SL2(R)
Vector space with generalized dot product
{\displaystyle W.} This construction is used in numerous contexts. The Gelfand–Naimark–Segal construction is a particularly important example of the use of this
Inner_product_space
corresponding GNS representation of A is a factor. Quantum state Gelfand–Naimark–Segal construction Quantum mechanics Quantum state Density matrix Lin,
State_(functional_analysis)
Representation of the symmetry group of spacetime in special relativity
Graev 1953 Gelfand & Naimark 1947 Takahashi 1963, p. 343. Knapp 2001, Equation 2.24. Folland 2015, Section 3.1. Folland 2015, Theorem 5.2. Tung 1985, Section
Representation theory of the Lorentz group
Representation_theory_of_the_Lorentz_group
Representation theory of the symplectic group
representations of the Weyl commutation relations. By Schur's lemma and the Gelfand–Naimark construction, the matrix coefficient of any vector determines the vector
Oscillator_representation
Surname list
shooter Wolfgang Sigl (born 1972), Austrian rower Brauer–Siegel theorem Gelfand–Naimark–Segal construction Siegel modular form Segal space Newell–Whitehead–Segel
Siegel
Conjecture linking two mathematical areas
{\displaystyle C^{*}} -algebra of the integers is by the commutative Gelfand–Naimark transform, which reduces to the Fourier transform in this case, isomorphic
Baum–Connes_conjecture
Topics referred to by the same term
an unrecognized provisional government of Libya Gelfand–Naimark–Segal construction, a theorem in functional analysis General News Service, a BBC-internal
GNS
Ukrainian-born Israeli mathematician
and Mathematics of the Odessa State University, with Mark Krein, Mark Naimark and Boris Yakovlevich Lewin as teachers. Krein was one of the major figures
Mikhail_Samuilovich_Livsic
*-algebra of bounded operators on a Hilbert space
representations, ergodic theory and quantum mechanics. His double commutant theorem shows that the analytic definition is equivalent to a purely algebraic
Von_Neumann_algebra
Mathematical entity to describe the probability of each possible measurement on a system
classes of algebras of observables. See State on a C*-algebra and Gelfand–Naimark–Segal construction for more details. Atomic electron transition Bloch sphere
Quantum_state
states. Given a there is a pure state f such that |f(a)| = ||a||. Gelfand–Naimark–Segal construction: If a JB algebra is isomorphic to the self-adjoint n
Jordan_operator_algebra
presence of a faithful semi-finite normal trace τ and the standard Gelfand–Naimark–Segal action of M on H = L2(M, τ), Edward Nelson proved that the measurable
Affiliated_operator
Part of spectral theory
hyperbolic space. More generally, the Plancherel theorem for SL(2,R) of Harish Chandra and Gelfand–Naimark can be deduced from Weyl's theory for the hypergeometric
Spectral theory of ordinary differential equations
Spectral_theory_of_ordinary_differential_equations
Group of real 2×2 matrices with unit determinant
unitary representations, which were worked out in detail by Gelfand and Naimark (1946), V. Bargmann (1947), and Harish-Chandra (1952). Linear group Special
SL2(R)
from the axioms of ZFC. In 1931, Kurt Gödel proved his incompleteness theorems, establishing that many mathematical theories, including ZFC, cannot prove
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
1936–1938 campaign in the Soviet Union
The national operations of the NKVD have been called genocidal; Norman Naimark called Stalin's policy towards Poles in the 1930s "genocidal", but he did
Great_Purge
Mathematical structures that allow quantum mechanics to be explained
subsystem when a PVM is performed on a larger, composite system (see Naimark's dilation theorem). The Schrödinger equation describes how a state vector evolves
Mathematical formulation of quantum mechanics
Mathematical_formulation_of_quantum_mechanics
American mathematician
115S. doi:10.1086/310698. Biography portal Mathematics portal Commutation theorem for traces Metaplectic group Symplectic group Symplectic spinor bundle
Irving_Segal
Universal construction of a complex Lie group from a real Lie group
202–203 See: Bump 2004 Zhelobenko 1973 Zhelobenko 1973 See: Gelfand & Naimark 1950, section 18, for SL(n,C) Bruhat 1956, p. 187 for SO(n,C) and Sp(n
Complexification_(Lie_group)
Notation for quantum states
"Hilbert space" can be broadened to accommodate these states (see the Gelfand–Naimark–Segal construction or rigged Hilbert spaces). Bra–ket notation continues
Bra–ket_notation
Matrix whose determinant is a resultant
Angew. Math., 53: 366–367, doi:10.1515/crll.1857.53.366 Kreĭn, M. G.; Naĭmark, M. A. (1981) [1936], "The method of symmetric and Hermitian forms in the
Bézout_matrix
German physicist (1901–1976)
(1969) The Alsos Mission. Award. pp. 219–241. Cassidy 1992, pp. 491–500 Naimark, Norman M. (1995) The Russians in Germany: A History of the Soviet Zone
Werner_Heisenberg
Theory of quantum gravity merging quantum mechanics and general relativity
Doubly special relativity – Generalization of special relativity Gelfand–Naimark–Segal construction – Correspondence in functional analysis Group field
Loop_quantum_gravity
1944), number theory Caryn Navy (born 1953), set-theoretic topology Mark Naimark (1909–1978), functional analysis and mathematical physics Zeev Nehari (1915–1978)
List_of_Jewish_mathematicians
Development of linear transformations forming the Lorentz group
Zeitschrift. 5 (14): 393–395. Ratcliffe (1994), 3.1 and Theorem 3.1.4 and Exercise 3.1 Naimark (1964), 2 in four dimensions Miller (1981), chapter 1 Miller
History of Lorentz transformations
History_of_Lorentz_transformations
NAIMARK THEOREM
NAIMARK THEOREM
Girl/Female
Arabic, Indian, Muslim, Tamil
Delight
Girl/Female
Muslim
Name of a mountain
Girl/Female
Afghan, African, American, Arabic, Assamese, Danish, Finnish, French, German, Hindu, Indian, Japanese, Kannada, Marathi, Muslim, Sanskrit, Sindhi, Swahili, Swedish, Tamil, Telugu
Belonging to One; Graceful; Comfort; Tranquil; To be Contented; Form of Naemi
Girl/Female
Tamil
Blessing, Living An enjoyable life, Belonging to one
Boy/Male
Tamil
Girl/Female
Muslim/Islamic
Tranquility
Girl/Female
Indian
Name of a mountain
Girl/Female
Basque Spanish
Refers to the Virgin Mary.
Boy/Male
Hindu
Girl/Female
Arabic, Muslim
Mountain
Girl/Female
Hindu
Blessing, Living An enjoyable life, Belonging to one
Girl/Female
Muslim
Comfort, Amenity, Tranquility, Peace, Living a soft, Enjoyable life
Girl/Female
Indian
Comfort, Amenity, Tranquility, Peace, Living a soft, Enjoyable life
Girl/Female
Arabic, Australian, Muslim
Blessing; Favour; Delight; Ease; Wealth
Girl/Female
Muslim
Blessing, Living An enjoyable life, Belonging to one
Girl/Female
Muslim/Islamic
Powerful strong minded person
NAIMARK THEOREM
NAIMARK THEOREM
Boy/Male
Indian
Spiritual teacher.
Girl/Female
Tamil
Queen
Surname or Lastname
English
English : variant of Goodrich.English : from the Middle English personal name Cuterich, Old English Cūðrīc, composed of the elements cūð ‘famous’, ‘well known’ + rīc ‘power’.
Surname or Lastname
English
English : unexplained. Apparently a metronymic from the female personal name Bess, pet form of Elizabeth.German : short form of Betz.In some cases it is probably an altered spelling of French Besse.
Boy/Male
Muslim/Islamic
Gift
Boy/Male
Tamil
Jagadbandu | ஜகதபஂதà¯
Lord Krishna
Boy/Male
British, English, Norse, Scandinavian
Swamp; From the Swampy Place
Girl/Female
French
Boy/Male
British, English
From the Church's Forest
Girl/Female
Welsh
Hateful.
NAIMARK THEOREM
NAIMARK THEOREM
NAIMARK THEOREM
NAIMARK THEOREM
NAIMARK THEOREM
n.
That which is considered and established as a principle; hence, sometimes, a rule.
n.
A statement of a principle to be demonstrated.
v. t.
To mark, as sheep, by cropping or slitting the ear.
a.
Alt. of Theorematical
n.
A mark cut into the ear of an animal to identify it; an earmark.
n.
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
a.
Theorematic.
n.
A mark to guide in traveling.
n.
A mark for identification; a distinguishing mark.
n.
A numerical coefficient in any particular case of the binomial theorem.
n.
One who constructs theorems.
a.
Of or pertaining to a theorem or theorems; comprised in a theorem; consisting of theorems.
n.
A theorem or proposition so easy of demonstration as to be almost self-evident.
p. pr. & vb. n.
of Earmark
a.
Containing many names or terms; multinominal; as, the polynomial theorem.
v. t.
To formulate into a theorem.
n.
A mark on the ear of sheep, oxen, dogs, etc., as by cropping or slitting.
imp. & p. p.
of Earmark