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