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Homological triviality of the category of L p -modules

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Abstract

The paper presents a complete description of topologically injective, topologically surjective, isometric and coisometric multiplication operators by a function acting between L p -spaces of σ-finite measure spaces. It is proved that all such operators are invertible from the right and from the left. As a corollary it is proved that in the category consisting of L p -spaces for all p ∈ [1,+∞] considered as left Banach modules over the algebra of bounded measurable functions, all objects are metrically and topologically projective, injective, and flat modules.

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References

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Authors and Affiliations

  1. Moscow State University, Faculty of Mechanics and Mathematics, Leninskie Gory, Moscow, 119991, Russia

    N. T. Nemesh

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

Additional information

Original Russian Text © N.T. Nemesh, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 4, pp. 3–12.

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Nemesh, N.T. Homological triviality of the category of L p -modules. Moscow Univ. Math. Bull. 71, 131–139 (2016). https://doi.org/10.3103/S002713221604001X

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  • DOI: https://doi.org/10.3103/S002713221604001X

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