On approximation properties of Pimsner algebras and crossed products by Hilbert bimodules

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Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$. Using a finite section method we construct a sequence of completely positive contractions factoring through matrix algebras over A which act on $s_ξ s_η^*$ as Schur multipliers converging to the identity. This shows immediately that for a finitely generated X the algebra $O_X$ inherits any standard approximation property such as nuclearity, exactness, CBAP or OAP from A. We generalise this to certain general Pimsner algebras by proving semi-splitness of the Toeplitz extension under certain conditions and discuss some examples.
11 pages, v2 has a modified title, abstract and introduction. The paper will appear in the Rocky Mountain Journal of Mathematics

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Operator Algebras, Functional Analysis, Primary 46L05, Secondary 46B28

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http://salesiana.dossiersoluciones.com/handle/123456789/157972

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0607628
 http://arxiv.org/abs/math/0607628

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arXiv