On operators with similar positive parts

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Let S=US|S| and T=UT|T| be the polar decompositions of S and T in L(H), respectively. We say that S and T have similar positive parts if |S| and |T| are similar. In this paper, we investigate properties of operators that are preserved under this similarity condition. We describe the form for the polar decomposition of an operator when the operator and its adjoint have similar positive parts. For this case, we also study the existence of invariant subspaces under this assumption.

Original languageEnglish
Pages (from-to)276-293
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Jul 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.


  • Polar decomposition
  • Similarity of positive parts
  • Spectral property


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