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• # Artykuł - szczegóły

## Banach Center Publications

2005 | 68 | 1 | 9-18

## Interpolation of the essential spectrum and the essential norm

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.

9-18

wydano
2005

### Twórcy

autor
• Department of Mathematics, Claremont McKenna College, Claremont, CA 91711, U.S.A.
autor
• Department of Mathematics and Statistics, P.O. Box 68, (Gustaf Hällströmin katu 2b), FIN-00014 University of Helsinki, Finland