Journal of Operator Theory

Volume 63, Issue 2, Spring 2010 pp. 375-388.

On the concept of absolutely continuous subspace for nonselfadjoint operators

Authors: Roman Romanov
Author institution: Laboratory of Quantum Networks, Institute for Physics, Saint Petersburg State University, St. Petersburg, 198504, Russia

Summary: 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.

Keywords: Absolutely continuous subspace, non-selfadjoint operators, weighted shift

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