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Non-trivial derivations on commutative regular algebras.

A. F. Ber, Vladimir I. Chilin, Fyodor A. Sukochev (2006)

Extracta Mathematicae

Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all...

Norm attaining bilinear forms on C*-algebras

J. Alaminos, R. Payá, A. R. Villena (2003)

Studia Mathematica

We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.

Normal cones and C * - m -convex structure

El Kinani, A., Mohamed Amine Nejjari, Mohamed Oudadess (2002)

Commentationes Mathematicae Universitatis Carolinae

The notion of normal cones is used to characterize C * - m -convex algebras among unital, symmetric and complete m -convex algebras.

Normes de Sobolev et convoluteurs bornés sur L 2 ( G )

P. Jolissaint, A. Valette (1991)

Annales de l'institut Fourier

Un groupe localement compact G muni d’une fonction-longueur L a la propriété ( D R ) par rapport à L si toute fonction à décroissance rapide sur G définit un convoluteur borné sur L 2 ( G ) . Nous donnons une condition suffisante assez générale pour que le couple ( G , L ) ait la propriété ( D R ) . Pour un tel couple, nous caractérisons les fonctions de type positif sur G faiblement associées à la représentation régulière gauche et, dans le cas discret, nous considérons les propriétés d’approximation de l’algèbre de Fourier...

Notes on a class of simple C*-algebras with real rank zero.

Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

A construction method is presented for a class of simple C*-algebras whose basic properties -including their real ranks- can be computed relatively easily, using linear algebra. A numerival invariant attached to the construction determines wether a given algebra has real rank 0 or 1. Moreover, these algebras all have stable rank 1, and each nonzero hereditary sub-C*-algebra contains a nonzero projection, yet there are examples in which the linear span of the projections is not dense. (This phenomenon...

Notes on automorphisms of ultrapowers of II₁ factors

David Sherman (2009)

Studia Mathematica

In functional analysis, approximative properties of an object become precise in its ultrapower. We discuss this idea and its consequences for automorphisms of II₁ factors. Here are some sample results: (1) an automorphism is approximately inner if and only if its ultrapower is ℵ₀-locally inner; (2) the ultrapower of an outer automorphism is always outer; (3) for unital *-homomorphisms from a separable nuclear C*-algebra into an ultrapower of a II₁ factor, equality of the induced traces implies unitary...

On 0 - 1 measure for projectors

Václav Alda (1980)

Aplikace matematiky

An example of a finite set of projectors in E 3 is exhibited for which no 0-1 measure exists.

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