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Relative Projectivity of the Modules \(L_p\)

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Abstract

In the paper, criteria are given for the relative projectivity of the \(L_p\)-spaces regarded as left Banach modules over the algebra of bounded measurable functions (\(1\le p\le+\infty\)) and the algebra of continuous functions vanishing at infinity (\(1\le p <+\infty\)).

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Notes

  1. Translator’s note: The translator prefers the construction “inner compactly regular” and similar constructions in items (v) and (vi) to the standard construction “inner regular with respect to compact sets” etc. used in [5] and other manuals.

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Funding

This work was supported by the Russian Foundation for Basic Research under grant 19–01–00447.

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Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, 119991, Russia

    N. T. Nemesh

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  1. N. T. Nemesh
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Correspondence to N. T. Nemesh.

Additional information

Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 93-106 https://doi.org/10.4213/mzm12994.

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Nemesh, N.T. Relative Projectivity of the Modules \(L_p\). Math Notes 111, 103–114 (2022). https://doi.org/10.1134/S0001434622010114

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  • DOI: https://doi.org/10.1134/S0001434622010114

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