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APPROXIMATELY BIPROJECTIVE BANACH ALGEBRAS AND NILPOTENT IDEALS

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  22 May 2012

HASAN POURMAHMOOD-AGHABABA
HASAN POURMAHMOOD-AGHABABA*
Affiliation:
Department of Mathematics, University of Tabriz, Tabriz, Iran School of Mathematics, Institute for Research in Fundamental Sciences (IPM), PO Box 19395-5746, Tehran, Iran (email: h_p_aghababa@tabrizu.ac.ir, h_pourmahmood@yahoo.com)
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Abstract

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By introducing a new notion of approximate biprojectivity we show that nilpotent ideals in approximately amenable or pseudo-amenable Banach algebras, and nilpotent ideals with the nilpotency degree larger than two in biflat Banach algebras cannot have the special property which we call ‘property (𝔹)’ (Definition 5.2 below) and hence, as a consequence, they cannot be boundedly approximately complemented in those Banach algebras.

Keywords

Banach algebrasbounded approximately complemented subspacesnilpotent idealsapproximate amenabilitypseudo-amenabilityapproximate biprojectivity

MSC classification

Secondary: 46H20: Structure, classification of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 158 - 173
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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