Numerical radius attaining compact linear operators
Angela Capel, Miguel Martin, Javier Meri
TL;DR
This paper demonstrates that certain compact linear operators on Banach spaces cannot be approximated by operators that attain their numerical radius, highlighting limitations in approximation properties.
Contribution
It provides a counterexample showing the non-density of numerical radius attaining operators among compact operators on Banach spaces.
Findings
Existence of compact operators not approximable by numerical radius attaining operators
Counterexample to the density of numerical radius attaining operators
Highlights limitations in approximation theory for operators
Abstract
We show that there are compact linear operators on Banach spaces which cannot be approximated by numerical radius attaining operators.
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