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arxiv: 0711.3557 · v2 · submitted 2007-11-22 · 🧮 math.FA · math-ph· math.MP

Notions of absolutely continuous subspace for nonselfadjoint operators

classification 🧮 math.FA math-phmath.MP
keywords absolutelycontinuousoperatorscompactcomponentscounterexampledifferentduality
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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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