Kth roots of p-hyponormal operators are subscalar operators of order 4k

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Abstract

In this paper, we consider the special case of the question raised by Halmos (see below). In particular, we show that if T k is p-hyponormal, then T is a subscalar operator of order 4k. As a corollary, we obtain that if T k is p-hyponormal and σ(T) has nonempty interior in the plane, then T has a nontrivial invariant subspace.

Original languageEnglish
Pages (from-to)173-187
Number of pages15
JournalIntegral Equations and Operator Theory
Volume59
Issue number2
DOIs
StatePublished - Oct 2007

Keywords

  • Invariant subspace
  • P-hyponormality
  • Subscalarity
  • The property (β)

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