Interpolation of S-numbers and entropy numbers of operators

Mieczysław Mastyło; Radosław Szwedek

doi:10.1215/17358787-2018-0046

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Home > Journals > Banach J. Math. Anal. > Volume 13 > Issue 2 > Article

April 2019 Interpolation of

S

-numbers and entropy numbers of operators

Mieczysław Mastyło, Radosław Szwedek

Banach J. Math. Anal. 13(2): 427-448 (April 2019). DOI: 10.1215/17358787-2018-0046

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Abstract

We introduce the notion of $\vec{s}$ -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.

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Mieczysław Mastyło. Radosław Szwedek. "Interpolation of $S$ -numbers and entropy numbers of operators." Banach J. Math. Anal. 13 (2) 427 - 448, April 2019. https://doi.org/10.1215/17358787-2018-0046