p-Quasihyponormal operators have scalar extensions of order 6

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Abstract

In this paper we show that every p-quasihyponormal operator has a scalar extension of order 6, i.e., is similar to the restriction to a closed invariant subspace of a scalar operator of order 6, where 0 < p < 1. As a corollary, we get that every p-quasihyponormal operator with rich spectra has a nontrivial invariant subspace. Also we show that Aluthge transforms preserve an analogue of the single-valued extension property for W2 (D, H) and an operator T.

Original languageEnglish
Pages (from-to)80-90
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume330
Issue number1
DOIs
StatePublished - 1 Jun 2007

Bibliographical note

Funding Information:
✩ This work was supported by a grant (R14-2003-006-01000-0) from Korea Research Foundation. E-mail address: eiko@ewha.ac.kr.

Keywords

  • Invariant subspaces
  • Scalar and subscalar operators
  • p-Quasihyponormal

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