Notions of absolutely continuous subspace for nonselfadjoint operators
Roman Romanov
TL;DR
This paper presents examples of nonselfadjoint operators demonstrating differences in weak and strong absolutely continuous subspaces and provides counterexamples to duality in spectral components, highlighting optimality within compact operators.
Contribution
It introduces specific examples illustrating the divergence of weak and strong absolutely continuous subspaces and addresses the duality problem in spectral theory for nonselfadjoint operators.
Findings
Operators with different weak and strong absolutely continuous subspaces
Counterexamples to the duality problem in spectral components
Optimal examples within the class of compact operators
Abstract
We give an example of an operator with different weak and strong absolutely continuous subspaces, and a counterexample to the duality problem for the spectral components. Both examples are optimal in the scale of compact operators.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Advanced Banach Space Theory