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Operators whose eigenvectors span the space. (English) Zbl 0812.47005

Summary: The operators on a complex separable Hilbert space \(H\) whose eigenvectors span \(H\) are investigated. They are shown to be hyperreflexive and some conditions under which such operators are reflexive are given. We recall an example of a non-reflexive operator whose commutant is reflexive.

MSC:

47A15 Invariant subspaces of linear operators
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