Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 343-360

INTERPOLATION OF APPROXIMATION NUMBERS BETWEEN HILBERT SPACES

Radoslaw Szwedek

A. Mickiewicz University, Faculty of Mathematics and Computer Science
Umultowska 87, 61-614 Poznan, Poland; szwedek 'at' amu.edu.pl

Abstract. We investigate whether the approximation numbers of operators behave well under the two-sided complex interpolation of Hilbert spaces. We study geometric interpolation of the approximation numbers as well as the entropy moduli. We also study geometric properties of the entropy and approximation numbers of operators between Hilbert spaces. In particular, we provide the quantitative estimates of approximation numbers as well as the interpolation results on normal operators.

2010 Mathematics Subject Classification: Primary 46B70, 47B06, 46B07, 47B15.

Key words: Approximation numbers, entropy numbers, interpolation spaces, quadratic interpolation, normal operators.

Reference to this article: R. Szwedek: Interpolation of approximation numbers between Hilbert spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), 343-360.

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doi:10.5186/aasfm.2015.4014