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DERIVATIONS OF FRÉCHET NUCLEAR GB$^{\ast }$-ALGEBRAS

Part of: Topological (rings and) algebras with an involution Topological algebras, normed rings and algebras, Banach algebras Selfadjoint operator algebras

Published online by Cambridge University Press:  04 June 2015

M. WEIGT  and
I. ZARAKAS
M. WEIGT
Affiliation:
Department of Mathematics and Applied Mathematics, Nelson Mandela Metropolitan University, Summerstrand Campus (South), Port Elizabeth 6031, South Africa email [email protected], [email protected]
I. ZARAKAS*
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 15784, Greece email [email protected]
*
✉[email protected]
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Abstract

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It is an open question whether every derivation of a Fréchet GB$^{\ast }$-algebra $A[{\it\tau}]$ is continuous. We give an affirmative answer for the case where $A[{\it\tau}]$ is a smooth Fréchet nuclear GB$^{\ast }$-algebra. Motivated by this result, we give examples of smooth Fréchet nuclear GB$^{\ast }$-algebras which are not pro-C$^{\ast }$-algebras.

Keywords

GB∗ -algebratopological algebraderivationlocally convex bimodulesmooth locally convex bimodule

MSC classification

Primary: 46H35: Topological algebras of operators
Secondary: 46H05: General theory of topological algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in or ) 46H40: Automatic continuity 46K05: General theory of topological algebras with involution 46L05: General theory of $C^*$-algebras 46L10: General theory of von Neumann algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 2 , October 2015 , pp. 290 - 301
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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