Chen, Yin On the Putnam–Fuglede theorem. (English) Zbl 1088.47027 Int. J. Math. Math. Sci. 2004, No. 53-56, 2821-2834 (2004). 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 \(S\Phi=\Phi T\). Reviewer: Armando R. Villena (Granada) MSC: 47B47 Commutators, derivations, elementary operators, etc. 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) Keywords:Putnam-Fuglede theorem; normal operator PDFBibTeX XMLCite \textit{Y. Chen}, Int. J. Math. Math. Sci. 2004, No. 53--56, 2821--2834 (2004; Zbl 1088.47027) Full Text: DOI EuDML