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Don Hadwin - Finitely strongly reductive operators

DON HADWIN, Mathematics Department, University of New Hampshire, Durham, New Hampshire  03824, USA
Finitely strongly reductive operators

Abstract: A Hilbert space operator is finitely strongly reductive ($\textrm{fsr}$) if every sequence of approximately invariant finite-dimensional subspaces is approximately reducing. Not every normal operator is $\textrm{fsr}$ (e.g., the approximate point spectrum must have empty interior), not every $\textrm{fsr}$ operator is normal ( e.g., isometries are $\textrm{fsr}$). We obtain some results (e.g., every essentially normal quasitriangular fsr operator is normal), and pose some interesting open problems.

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