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On the Putnam–Fuglede theorem. (English) Zbl 1088.47027

The author extends the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to some non-normal operators. One of the results states that if \(S, T\) are normal operators, \(P, Q\) are quasinilpotent operators such that \(SP=PS\), \(TQ=QT\), and \(\Phi\) is an operator with \((S+P)\Phi=\Phi(T+Q)\), then \(S\Phi=\Phi T\).

MSC:

47B47 Commutators, derivations, elementary operators, etc.
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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