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article · Moscow University Mathematics Bulletin · 2016

Homological triviality of the category of L p -modules

N. T. Nemesh

Cited by 0Abstract and details only

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.

Cite this paper

APA 7

Nemesh, N. T. (2016). Homological triviality of the category of L p -modules. Moscow University Mathematics Bulletin, 71(4), 131–139. https://doi.org/10.3103/s002713221604001x

MLA 9

Nemesh, N. T. “Homological triviality of the category of L p -modules.” Moscow University Mathematics Bulletin, vol. 71, no. 4, 2016, pp. 131–39, https://doi.org/10.3103/s002713221604001x.

Chicago

Nemesh, N. T. 2016. “Homological triviality of the category of L p -modules.” Moscow University Mathematics Bulletin 71 (4): 131–39. https://doi.org/10.3103/s002713221604001x.

Harvard

Nemesh, N.T. (2016) ‘Homological triviality of the category of L p -modules’, Moscow University Mathematics Bulletin, 71(4), pp. 131–139. Available at: https://doi.org/10.3103/s002713221604001x.

BibTeX
@article{nemesh2016homological,
  title = {{Homological triviality of the category of L p -modules}},
  author = {Nemesh, N. T.},
  journal = {Moscow University Mathematics Bulletin},
  volume = {71},
  number = {4},
  pages = {131--139},
  year = {2016},
  doi = {10.3103/s002713221604001x}
}

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