This is an announcement for the paper "Norm attaining operators and pseudospectrum" by Stanislav Shkarin.

Abstract: It is shown that if $1<p<\infty$ and $X$ is a subspace or a quotient of an $\ell_p$-direct sum of finite dimensional Banach spaces, then for any compact operator $T$ on $X$ such that $|I+T|>1$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $|I+T|>1$ and $I+T$ does not attain its norm.

Archive classification: math.FA

Mathematics Subject Classification: 47A30, 47A10

Citation: Integral Equations and Operator Theory 64 (2009), 115-136

Submitted from: s.shkarin@qub.ac.uk

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1209.1218

or

http://arXiv.org/abs/1209.1218