Abstract
Several necessary conditions for the topological flatness of Banach modules are given. The main result is as follows: a Banach module over a relatively amenable Banach algebra which is topologically flat as a Banach space is topologically flat as a Banach module. Finally examples of topologically flat modules among classical modules of analysis are given.
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Text Copyright © The Author(s), 2019. Published in Funktsional’nyi Analiz i Ego Prilozheniya, 2019, Vol. 53, No. 2, pp. 32–41.
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Nemesh, N.T. Topologically Flat Banach Modules. Funct Anal Its Appl 53, 102–109 (2019). https://doi.org/10.1134/S0016266319020035
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DOI: https://doi.org/10.1134/S0016266319020035