Backward Aluthge iterates of a hyponormal operator have scalar extensions

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Abstract

The backward Aluthge iterate (defined below) of a hyponormal operator was initiated in [11]. In this paper we characterize the backward Aluthge iterate of a weighted shift. Also we show that the backward Aluthge iterate of a hyponormal operator has an analogue of the single valued extension property for W2k + 2 (D, H). Finally, we show that backward Aluthge iterates of a hyponormal operator have scalar extensions. As a corollary, we get that the backward Aluthge iterate of a hyponormal operator has a nontrivial invariant subspace if its spectrum has interior in the plane.

Original languageEnglish
Pages (from-to)567-582
Number of pages16
JournalIntegral Equations and Operator Theory
Volume57
Issue number4
DOIs
StatePublished - Apr 2007

Keywords

  • Aluthge transforms
  • Backward Aluthge iterates
  • Subscalar operators
  • The property (β)

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