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Finite generation in C*-algebras and Hilbert C*-modules

David P. Blecher, Tomasz Kania (2014)

Studia Mathematica

We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.

Finite rank approximation and semidiscreteness for linear operators

Christian Le Merdy (1999)

Annales de l'institut Fourier

Given a completely bounded map u : Z M from an operator space Z into a von Neumann algebra (or merely a unital dual algebra) M , we define u to be C -semidiscrete if for any operator algebra A , the tensor operator I A u is bounded from A min Z into A nor M , with norm less than C . We investigate this property and characterize it by suitable approximation properties, thus generalizing the Choi-Effros characterization of semidiscrete von Neumann algebras. Our work is an extension of some recent work of Pisier on an analogous...

Finite sums and products of commutators in inductive limit C * -algebras

Klaus Thomsen (1993)

Annales de l'institut Fourier

Results of T. Fack, P. de la Harpe and G. Skandalis concerning the internal structure of simple A F -algebras are extended to C * -algebras that are inductive limits of finite direct sums of homogeneous C * -algebras. The generalizations are obtained with slightly varying assumptions on the building blocks, but all results are applicable to unital simple inductive limits of finite direct sums of circle algebras.

First order calculi with values in right-universal bimodules

Andrzej Borowiec, Vladislav Kharchenko, Zbigniew Oziewicz (1997)

Banach Center Publications

The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.

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