Yuan-Hang Zhang

The Stability and Density of Norm Attaining Operators on Reducing Subspaces

For a bounded linear operator on an infinite-dimensional Hilbert space, we consider the class $\beta(H)$ of operators whose restrictions to all nonzero reducing subspaces attain their norms. We prove that $\beta(H)$ is dense in $\mathcal{B}(H)$ in the operator norm. Since $\beta(H)$ is not stable under arbitrary compac...