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Measures of non-compactness in Orlicz modular spaces.

A. G. Aksoy;  J.-B. Baillon — 1993

Collectanea Mathematica

In this paper we show that the ball-measure of non-compactness of a norm bounded subset of an Orlicz modular space L-Psi is equal to the limit of its n-widths. We also obtain several inequalities between the measures of non-compactness and the limit of the n-widths for modular bounded subsets of L-Psi which do not have Delta-2-condition. Minimum conditions on Psi to have such results are specified and an example of such a function Psi is provided.

Interpolation of the essential spectrum and the essential norm

A. G. Aksoy;  H.-O. Tylli — 2005

Banach Center Publications

The behavior of the essential spectrum and the essential norm under (complex/real) interpolation is investigated. We extend an example of Albrecht and Müller for the spectrum by showing that in complex interpolation the essential spectrum σ e ( S [ θ ] ) of an interpolated operator is also in general a discontinuous map of the parameter θ. We discuss the logarithmic convexity (up to a multiplicative constant) of the essential norm under real interpolation, and show that this holds provided certain compact approximation...

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