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2 results

  • Square roots of weighted shifts of multiplicity two

  • Part of
  • Chanaka Kottegoda, Trieu Le, Tomas Miguel Rodriguez
  • Journal:
    Canadian Mathematical Bulletin / Volume 66 / Issue 3 / September 2023
    Published online by Cambridge University Press:
    23 December 2022, pp. 791-807
    Print publication:
    September 2023
    • Article
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      • Open access
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  • Given a weighted shift T of multiplicity two, we study the set $\sqrt {T}$ of all square roots of T. We determine necessary and sufficient conditions on the weight sequence so that this set is non-empty. We show that when such conditions are satisfied, $\sqrt {T}$ contains a certain special class of operators. We also obtain a complete description of all operators in $\sqrt {T}$.

  • A NOTE ON POSITIVE ${\mathcal{A}}{\mathcal{N}}$ OPERATORS

  • Part of
  • IAN DOUST
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 100 / Issue 1 / August 2019
    Published online by Cambridge University Press:
    26 December 2018, pp. 129-130
    Print publication:
    August 2019
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  • We show that positive absolutely norm attaining operators can be characterised by a simple property of their spectra. This result clarifies and simplifies a result of Ramesh. As an application we characterise weighted shift operators which are absolutely norm attaining.