Subscalarity of operator transforms

Sungeun Jung, Eungil Ko, Shinhae Park

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper, we provide various connections between a bounded linear operator T and some of its transforms, namely the Aluthge transform (Formula presented.), Duggal transform (Formula presented.), and mean transform (Formula presented.). In particular, we show that under the condition that ǀTǀUǀTǀ = ǀTǀ2U where T = UǀTǀ is the polar decomposition, if one of T, (Formula presented.), and (Formula presented.) is subscalar of finite order, then (Formula presented.) is also subscalar of finite order. As an application, we find subscalar operator matrices. We also give several spectral relations. Finally, we provide an equivalent condition under which a weighted shift has a hyponormal iterated mean transform.

Original languageEnglish
Pages (from-to)2042-2056
Number of pages15
JournalMathematische Nachrichten
Volume288
Issue number17-18
DOIs
StatePublished - 1 Dec 2015

Bibliographical note

Publisher Copyright:
© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Keywords

  • Aluthge transform
  • Duggal transform
  • invariant subspace
  • Mean transform
  • subscalar operator

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