Displaying similar documents to “Extensions of certain real rank zero C * -algebras”

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

Kenneth R. Goodearl (1992)

Publicacions Matemàtiques

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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....

Unital extensions of A F -algebras by purely infinite simple algebras

Junping Liu, Changguo Wei (2014)

Czechoslovak Mathematical Journal

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In this paper, we consider the classification of unital extensions of A F -algebras by their six-term exact sequences in K -theory. Using the classification theory of C * -algebras and the universal coefficient theorem for unital extensions, we give a complete characterization of isomorphisms between unital extensions of A F -algebras by stable Cuntz algebras. Moreover, we also prove a classification theorem for certain unital extensions of A F -algebras by stable purely infinite simple C * -algebras...

A double commutant theorem for purely large C*-subalgebras of real rank zero corona algebras

P. W. Ng (2009)

Studia Mathematica

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Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.

The Order on Projections in C*-Algebras of Real Rank Zero

Tristan Bice (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove a number of fundamental facts about the canonical order on projections in C*-algebras of real rank zero. Specifically, we show that this order is separative and that arbitrary countable collections have equivalent (in terms of their lower bounds) decreasing sequences. Under the further assumption that the order is countably downwards closed, we show how to characterize greatest lower bounds of finite collections of projections, and their existence, using the norm and spectrum...