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Nice connecting paths in connected components of sets of algebraic elements in a Banach algebra

Endre Jr. Makai, Jaroslav Zemánek (2016)

Czechoslovak Mathematical Journal

Generalizing earlier results about the set of idempotents in a Banach algebra, or of self-adjoint idempotents in a C * -algebra, we announce constructions of nice connecting paths in the connected components of the set of elements in a Banach algebra, or of self-adjoint elements in a C * -algebra, that satisfy a given polynomial equation, without multiple roots. In particular, we prove that in the Banach algebra case every such non-central element lies on a complex line, all of whose points satisfy the...

Non-commutative Gelfand-Naimark theorem

Janusz Migda (1993)

Commentationes Mathematicae Universitatis Carolinae

We show that if Y is the Hausdorffization of the primitive spectrum of a C * -algebra A then A is * -isomorphic to the C * -algebra of sections vanishing at infinity of the canonical C * -bundle over Y .

Non-normal elements in Banach *-algebras

B. Yood (2004)

Studia Mathematica

Let A be a Banach *-algebra with an identity, continuous involution, center Z and set of self-adjoint elements Σ. Let h ∈ Σ. The set of v ∈ Σ such that (h + iv)ⁿ is normal for no positive integer n is dense in Σ if and only if h ∉ Z. The case where A has no identity is also treated.

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...

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