In mathematics, the Gelfand representation in functional analysis (named after I. M. Gelfand) is either of two things: a way of representing commutative...

theory; the Gelfand–Naimark theorem; the Gelfand–Naimark–Segal construction; Gelfand–Shilov spaces; the Gelfand–Pettis integral; the representation theory...

{\displaystyle *} -representation from the state. It is named for Israel Gelfand, Mark Naimark, and Irving Segal. A ∗ {\displaystyle *} -representation of a C ∗...

and πf is the irreducible representation associated to f by the GNS construction. Thus the Gelfand–Naimark representation acts on the Hilbert direct...

homeomorphism) locally compact Hausdorff space X. This is shown using the Gelfand representation. The notion of local compactness is important in the study of topological...

In representation theory, a branch of mathematics, the Gelfand–Graev representation is a representation of a reductive group over a finite field introduced...

normal, the Gelfand representation is isometric; in particular, it is injective and its image is closed. But the image of the Gelfand representation is dense...

definition of Gelfand pair is roughly that the restriction to K of any irreducible representation of G contains the trivial representation of K with multiplicity...

a grandson of Israel Gelfand Vladimir Gelfand, a Soviet-Jewish writer Named after Israel Gelfand: the Gelfand representation allows a complete characterization...

The Gelfand–Naimark–Segal construction embeds any C*-algebra in an algebra of bounded operators on some Hilbert space. The Gelfand representation (also...

Gelfand, major contributor to numerous areas of mathematics, including group theory, representation theory and linear algebra, author of the Gelfand representation...

algebra reflexive operator algebra Calkin algebra Gelfand representation Gelfand–Naimark theorem Gelfand–Naimark–Segal construction Von Neumann algebra Abelian...

one-dimensional subspaces. In this way Gelfand and Tsetlin were able to obtain a basis of any irreducible representation of U ( N ) {\displaystyle U(N)} or...

now called non-commutative spaces. This is by analogy with the Gelfand representation, which shows that commutative C*-algebras are dual to locally compact...

functions over a compact space, this turns it into a C* algebra (cf. Gelfand representation). The uniform metric between two bounded functions f , g : X → Y...

M. A survey paper from 1975 of the subject by Anatoly Vershik, Israel Gelfand and M. I. Graev attributes the original interest in the topic to research...

maximal ideals. This is the Gelfand representation. In lattice theory, there are a number of dualities, based on representation theorems that connect certain...

f K } {\displaystyle \{f_{K}\}} is an approximate identity. The Gelfand representation states that every commutative C*-algebra is *-isomorphic to the...

continuous functions, which determine the group completely. Gelfand–Naimark theorem Representation theory И. М. Гельфанд, Д. А. Райков, Неприводимые унитарные...

Representation theory. A first course, Graduate Texts in Mathematics, vol. 129, New York: Springer-Verlag, ISBN 978-0-387-97495-8, MR 1153249 Gelfand...

{A}}=C^{*}(a,e)} . The actual construction is almost immediate from the Gelfand representation: it suffices to assume A {\displaystyle {\mathcal {A}}} is the C*-algebra...

viewed as noncommutative generalizations of probability measures. By Gelfand representation, every commutative C*-algebra A is of the form C0(X) for some locally...

off. This equation is derived from the Gelfand–Levitan integral equation, using the Povzner–Levitan representation. Suppose that for a potential u ( x )...

address Banach algebras in general. This development leads to the Gelfand representation, which covers the commutative case, and further into non-commutative...

Gelfand, major contributor to numerous areas of mathematics, including group theory, representation theory and linear algebra, author of the Gelfand representation...

In the mathematical field of representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra...

In mathematics, a rigged Hilbert space (Gelfand triple, nested Hilbert space, equipped Hilbert space) is a construction designed to link the distribution...

spectrum of a linear operator; see Spectrum of a C*-algebra and Gelfand representation. Matsumura 1989, p. 143, §7, Remarks Matsumura 1989, §19, Theorem...

Israel Gelfand, contributed to many areas of mathematics, including group theory, representation theory and linear algebra, author of the Gelfand representation...

irreducible 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...