ON SOME CLASS OF INTERPOLATION FUNCTORS


Cite item

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 Federation

References

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Copyright (c) 2019 С. В. Асташкин

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