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Stability of Real C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Jeffrey L. Boersema  and
Efren Ruiz
Jeffrey L. Boersema
Affiliation:
Department of Mathematics, Seattle University, Seattle, WA 98122, U.S.A.e-mail: boersema@seattleu.edu
Efren Ruiz
Affiliation:
Department of Mathematics, University of Hawaii Hilo, Hilo, Hawaii 96720, U.S.A.e-mail: ruize@hawaii.edu
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Abstract

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We will give a characterization of stable real ${{C}^{*}}$-algebras analogous to the one given for complex ${{C}^{*}}$-algebras by Hjelmborg and Rørdam. Using this result, we will prove that any real ${{C}^{*}}$-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real ${{C}^{*}}$-algebras satisfying the corona factorization property include $\text{AF}$-algebras and purely infinite C*-algebras. We will also provide an example of a simple unstable C*-algebra, the complexification of which is stable.

Keywords

46L05stabilityreal C*-algebras
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 593 - 606
Copyright
Copyright © Canadian Mathematical Society 2011

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