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ON SOME CLASS OF INTERPOLATION FUNCTORS
- Authors: Astashkin S.V.1
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Affiliations:
- Samara National Research University
- Issue: Vol 25, No 2 (2019)
- Pages: 7-20
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/7475
- DOI: https://doi.org/10.18287/2541-7525-2019-25-2-7-20
- ID: 7475
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Abstract
As it is well known, the Gustavsson — Peetre construction, using the concept of unconditional convergence in Banach spaces, provides an important class of interpolation functors. In this paper, we define a new close construction, based on the use of the so-called random unconditional convergence. We find necessary and sufficient conditions, which being imposed on a generating function give us an interpolation functor defined on the category of Banach couples. It is shown that calculating the latter functor for a couple of Orlicz spaces results in the ”natural” interpolation theorem. Moreover, we obtain conditions that guarantee the coincidence of this functor with the corresponding Gustavsson — Peetre functor, as well as with the Calder´on — Lozanovskii method.
About the authors
S. V. Astashkin
Samara National Research University
Author for correspondence.
Email: morenov@ssau.ru
ORCID iD: 0000-0002-8239-5661
Doctor of Physical and Mathematical Sciences, professor, Head of the Department of Functional Analysis and Function Theory
Russian FederationReferences
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