Banach Journal of Mathematical Analysis

Interpolation of S-numbers and entropy numbers of operators

Mieczysław Mastyło and Radosław Szwedek

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Abstract

We introduce the notion of s -numbers for operators in Banach couples. We investigate variants of the approximation, Gelfand, and Kolmogorov numbers. In particular, we derive upper estimates of these numbers for operators between spaces generated by interpolation functors on Banach couples satisfying interpolation variants of approximation properties. We also study two-sided interpolation of entropy numbers.

Article information

Source
Banach J. Math. Anal., Volume 13, Number 2 (2019), 427-448.

Dates
Received: 19 August 2018
Accepted: 5 December 2018
First available in Project Euclid: 27 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1551258125

Digital Object Identifier
doi:10.1215/17358787-2018-0046

Mathematical Reviews number (MathSciNet)
MR3927881

Zentralblatt MATH identifier
07045466

Subjects
Primary: 46B70: Interpolation between normed linear spaces [See also 46M35]
Secondary: 47B07: Operators defined by compactness properties 47B38: Operators on function spaces (general) 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)

Keywords
entropy numbers s-numbers interpolation functor interpolation spaces

Citation

Mastyło, Mieczysław; Szwedek, Radosław. Interpolation of $S$ -numbers and entropy numbers of operators. Banach J. Math. Anal. 13 (2019), no. 2, 427--448. doi:10.1215/17358787-2018-0046. https://projecteuclid.org/euclid.bjma/1551258125


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