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Module approximate biprojectivity and module approximate biflatness of Banach algebras

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Abstract

In this paper, in analogy with the classical case, we introduce module approximately biprojective and module approximately biflat Banach algebras. For an inverse semigroup S with the set of idempotents E, we show that the concepts of module approximate biprojectivity and module pseudo-amenability for \(l^1(S,\omega )\) coincide (as an \(l^1(E)\)-module). We also find necessary and sufficient conditions for the weighted semigroup algebra \(l^{1}(S,\omega )\) to be module approximately biprojective and module approximately biflat. Finally, we study the module cohomological properties of projective tensor product of Banach algebras.

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Acknowledgements

The authors express their sincere thanks to the reviewer for the careful and detailed reading of the manuscript and very helpful suggestions that improved the manuscript substantially.

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Authors and Affiliations

  1. Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran

    Abasalt Bodaghi

  2. Esfarayen University of Technology, Esfarayen, North Khorasan, Iran

    Somaye Grailoo Tanha

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  1. Abasalt Bodaghi
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  2. Somaye Grailoo Tanha
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Correspondence to Abasalt Bodaghi.

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Bodaghi, A., Grailoo Tanha, S. Module approximate biprojectivity and module approximate biflatness of Banach algebras. Rend. Circ. Mat. Palermo, II. Ser 70, 409–425 (2021). https://doi.org/10.1007/s12215-020-00503-8

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