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Bibliographic Details
Main Author: Pustylnik, Evgeniy
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2605.00530
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author Pustylnik, Evgeniy
author_facet Pustylnik, Evgeniy
contents We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. Our approach consists of two features. Applying the principle "reductio ad absurdum," we obtain a possibility to carry out all proofs only for some specially constructed subspaces of the given spaces, e.g., having a common Schauder basis. As a second feature, we consider in all assertions only embedding operators obtaining the full result just at the end of the paper. No analytical presentation of operators, spaces and interpolation functors is required and the complex method is admissible as a particular case.
format Preprint
id arxiv_https___arxiv_org_abs_2605_00530
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A new approach to interpolation of compact linear operators
Pustylnik, Evgeniy
Functional Analysis
46B50, 46B70
We prove an abstract theorem on keeping the compactness property of a linear operator after interpolation in Banach spaces. Our approach consists of two features. Applying the principle "reductio ad absurdum," we obtain a possibility to carry out all proofs only for some specially constructed subspaces of the given spaces, e.g., having a common Schauder basis. As a second feature, we consider in all assertions only embedding operators obtaining the full result just at the end of the paper. No analytical presentation of operators, spaces and interpolation functors is required and the complex method is admissible as a particular case.
title A new approach to interpolation of compact linear operators
topic Functional Analysis
46B50, 46B70
url https://arxiv.org/abs/2605.00530