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Operator Algebras, Operator Theory and Applications pp 295–308Cite as

On Homotopical Non-invertibility of C*-extensions

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 181))

Abstract

We have presented recently an example of a C*-extension, which is not invertible in the semigroup of homotopy classes of C*-extensions. Here we reveal the cause for existence of homotopy non-invertible C*-extensions: it is related to non-exact C*-algebras and to possibility to distinguish different tensor C*-norms by K-theory. We construct a special C*-algebra, K-theory of which hosts an obstruction for homotopical non-invertibility, and show that this obstruction for our example does not vanish.

Research was partially supported by RFFI grant 05-01-00923.

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Author information

Authors and Affiliations

  1. Dept. of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119992, Russia

    Vladimir Manuilov

  2. Harbin Institute of Technology, P. R. China

    Vladimir Manuilov

Authors
  1. Vladimir Manuilov
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Editor information

Editors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, U.T.L., Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

    Maria Amélia Bastos , Amarino Brites Lebre  & Frank-Olme Speck ,  & 

  2. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Israel

    Israel Gohberg

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© 2008 Birkhäuser Verlag Basel/Switzerland

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Manuilov, V. (2008). On Homotopical Non-invertibility of C*-extensions. In: Bastos, M.A., Lebre, A.B., Speck, FO., Gohberg, I. (eds) Operator Algebras, Operator Theory and Applications. Operator Theory: Advances and Applications, vol 181. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8684-9_14

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