Interpolation of the essential spectrum and the essential norm

A. G. Aksoy, and H.-O. Tylli. "Interpolation of the essential spectrum and the essential norm." Banach Center Publications 68.1 (2005): 9-18. <http://eudml.org/doc/282005>.

@article{A2005,
abstract = {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.},
author = {A. G. Aksoy, H.-O. Tylli},
journal = {Banach Center Publications},
keywords = {essential spectrum; essential norm; complex interpolation; real interpolation},
language = {eng},
number = {1},
pages = {9-18},
title = {Interpolation of the essential spectrum and the essential norm},
url = {http://eudml.org/doc/282005},
volume = {68},
year = {2005},
}

TY - JOUR
AU - A. G. Aksoy
AU - H.-O. Tylli
TI - Interpolation of the essential spectrum and the essential norm
JO - Banach Center Publications
PY - 2005
VL - 68
IS - 1
SP - 9
EP - 18
AB - 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.
LA - eng
KW - essential spectrum; essential norm; complex interpolation; real interpolation
UR - http://eudml.org/doc/282005
ER -