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Approximate characterizations of projectivity and injectivity for Banach modules

Published online by Cambridge University Press:  01 September 2007

A. YU. PIRKOVSKII
A. YU. PIRKOVSKII*
Affiliation:
Department of Nonlinear Analysis and Optimization, Faculty of Science, Peoples' Friendship University of Russia, Mikluho-Maklaya 6, 117198 Moscow, Russia. email: pirkosha@sci.pfu.edu.ru, pirkosha@online.ru
*
†Address for correspondence: Krupskoi 8-3-89, 119311 Moscow, Russia.
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Abstract

We characterize projective and injective Banach modules in approximate terms, generalizing thereby a characterization of contractible Banach algebras given by F. Ghahramani and R. J. Loy. As a corollary, we show that each uniformly approximately amenable Banach algebra is amenable. Some applications to homological dimensions of Banach modules and algebras are also given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 375 - 385
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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