Supporting sequences of pure states on JB algebras

Jan Hamhalter

Displaying similar documents to “Supporting sequences of pure states on JB algebras”

Pure states on Jordan algebras

Jan Hamhalter (2001)

Mathematica Bohemica

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We prove that a pure state on a ȁlgebra or a JB algebra is a unique extension of some pure state on a singly generated subalgebra if and only if its left kernel has a countable approximative unit. In particular, any pure state on a separable JB algebra is uniquely determined by some singly generated subalgebra. By contrast, only normal pure states on JBW algebras are determined by singly generated subalgebras, which provides a new characterization of normal pure states. As an application...

A new proof of the noncommutative Banach-Stone theorem

David Sherman (2006)

Banach Center Publications

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Surjective isometries between unital C*-algebras were classified in 1951 by Kadison [K]. In 1972 Paterson and Sinclair [PS] handled the nonunital case by assuming Kadison’s theorem and supplying some supplementary lemmas. Here we combine an observation of Paterson and Sinclair with variations on the methods of Yeadon [Y] and the author [S1], producing a fundamentally new proof of the structure of surjective isometries between (nonunital) C*-algebras. In the final section we indicate...

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

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A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{\infty}$ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

Finite sums of commutators in $C^{*}$ -algebras

Thierry Fack (1982)

Annales de l'institut Fourier

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We prove that for many $C^{*}$ -algebras, the null space of all finite traces is spanned by finite sums of commutators.

Generalized Post algebras and their application to some infinitary many-valued logics

Cat-Ho Nguyen

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CONTENTSIntroduction............................................................................................................................................................................... 5Part I. A generalization of Post algebras............................................................................................................................. 7 1. Definition and characterization of generalized Post algebras............................................. 7 2. Post...

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

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In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

Some remarks on $Q$ -algebras

Nicolas Th. Varopoulos (1972)

Annales de l'institut Fourier

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We study Banach algebras that are quotients of uniform algebras and we show in particular that the class is stable by interpolation. We also show that $ℓ^{p}$ , $(1 \leq p \leq \infty)$ are $Q$ algebras and that $A_{n} = ℨ L^{1} (Z; 1 + | n |^{α})$ is a $Q$ -algebra if and only if $α > 1 / 2$ .

Metric generalizations of Banach algebras

W. Żelazko

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CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

A characterization of essential sets of function algebras

Jan Čerych (2004)

Archivum Mathematicum

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In the present note, we characterize the essential set $E$ of a function algebra $A$ defined on a compact Hausdorff space $X$ in terms of local properties of functions in $A$ at the points off $E$ .