Interpolation of the essential spectrum and the essential norm

• Autorzy: A. G. Aksoy , H.-O. Tylli
• Języki publikacji: EN

Abstrakty

EN

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 conditions are satisfied. Some evidence supporting a counterexample is presented.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 46B70: Interpolation between normed linear spaces
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2005
• Tom: 68
• Numer: 1
• Strony: 9-18

Daty

wydano

2005

Twórcy

autor

A. G. Aksoy

• Department of Mathematics, Claremont McKenna College, Claremont, CA 91711, U.S.A.

autor

H.-O. Tylli

• Department of Mathematics and Statistics, P.O. Box 68, (Gustaf Hällströmin katu 2b), FIN-00014 University of Helsinki, Finland

Identyfikatory

DOI

10.4064/bc68-0-1