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arXiv · 2109.05968

General Theorem on Interpolation of Compact Operators

Evgeniy Pustylnik
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Abstract

We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. No analytical presentation of operators, spaces and interpolation functor is required. We use only some little-known properties of compact sets and various facts about bases and basic sequences (with detailed references to the monograph "Bases in Banach spaces", Vol. I-II by I.M. Singer). Therefore the results are applicable to arbitrary spaces and any interpolation functor, including the complex method. The "two-sided" compactness is also mentioned at the end of this paper as a mere corollary.

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BibTeXRIS

Evgeniy Pustylnik. 2021-09-10. General Theorem on Interpolation of Compact Operators. https://arxiv.org/abs/2109.05968

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