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Generalized spherical Aluthge transforms and binormality for commuting pairs of operators

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  • Slaviša Djordjević
  • Jaewoong Kim
  • Jasang Yoon

Abstract

In this paper, we introduce the notion of generalized spherical Aluthge transforms for commuting pairs of operators and study nontrivial joint invariant (resp. hyperinvariant) subspaces between the generalized spherical Aluthge transform and the original commuting pair. Next, we study the norm continuity through generalized Aluthge transform maps. We also study how the Taylor spectra and the Fredrolm index of commuting pairs of operators behave under the spherical Duggal transform. Finally, we introduce the notion of Campbell binormality for commuting pairs of operators and investigate some of its basic properties under spherical Aluthge and Duggal transforms. Moreover, we obtain new set inclusion diagrams among normal, quasinormal, centered, and Campbell binormal commuting pairs of operators.

Suggested Citation

  • Slaviša Djordjević & Jaewoong Kim & Jasang Yoon, 2023. "Generalized spherical Aluthge transforms and binormality for commuting pairs of operators," Mathematische Nachrichten, Wiley Blackwell, vol. 296(7), pages 2734-2757, July.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:7:p:2734-2757
    DOI: 10.1002/mana.202100320
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