, Volume 19, Issue 4, pp 911–925 | Cite as

On Fuglede–Putnam properties

  • Seonjin Jo
  • Yoenha Kim
  • Eungil Ko


In this paper, we study the Fuglede–Putnam property. We give a necessary and sufficient condition for which \((\oplus _{i=1}^{n}A_i,\oplus _{i=1}^{n}B_i)\) satisfies the Fuglede–Putnam property. We also study the local spectral theory associated with the Fuglede–Putnam property. Finally, we define the weak Fuglede–Putnam property and we investigate several cases which satisfy the weak Fuglede–Putnam property.


Fuglede–Putnam theorem Commutator Generalized commutator Aluthge transform Normal operator 

Mathematics Subject Classification

47A50 47A63 



The authors wish to thank the referee for a careful reading and valuable comments for the original draft.


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsEwha Womans UniversitySeoulKorea
  2. 2.Institute of Mathematical SciencesEwha Womans UniversitySeoulKorea

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