Fuglede–Putnam theorem for \((\alpha , \beta )\)-normal operators

  • A. BachirEmail author
  • T. Prasad


In this paper, we obtain some properties of \((\alpha , \beta )\)-normal and we prove following assertions.
  1. (i)

    If T is \((\alpha , \beta )\)-normal operator, S is an invertible operator and X is a Hilbert–Schmidt operator such that \(TX=XS\), then \(T^{*}X=XS^{*}\).

  2. (ii)

    If T is totally \((\alpha , \beta )\)-normal operator, then the range of generalized derivation \(\delta _{T}: \mathcal {B}( {\mathcal H}) \ni X \rightarrow TX- XT \in \mathcal {B}( {\mathcal H}) \) is orthogonal to its kernel.



Fuglede–Putnam theorem Hyponormal operator \((\alpha</Keyword> <Keyword>\beta )\)-Normal operator Orthogonality 

Mathematics Subject Classification

47B20 47A10 



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Authors and Affiliations

  1. 1.Department of MathematicsKing Khalid UniversityAbhaSaudi Arabia
  2. 2.Department of MathematicsCochin University of Science and TechnologyCochin-22India

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