Operator equations and subscalarity

Sungeun Jung, Eungil Ko

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the system of operator equations ABA = A2 and BAB = B2. Let (A, B) be a solution to this system. We give several connections among the operators A, B, AB, and BA. We first prove that A is subscalar of finite order if and only if B is, which is equivalent to the subscalarity of AB or BA with finite order. As a corollary, if A is subscalar and its spectrum has nonempty interior, then B has a nontrivial invariant subspace. We also provide examples of subscalar operator matrices. Moreover, we deal with algebraicity, power boundedness, and quasitriangularity, using some power properties obtained from the operator equations.

Original languageEnglish
Pages (from-to)97-113
Number of pages17
JournalStudia Mathematica
Volume225
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Bishop's property (β)
  • Invariant subspace
  • Subscalar

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