Spectrum of weighted composition operators part V spectrum and essential spectra of weighted rotation-like operators

Abstract

We introduce the class of weighted “rotation-like” operators and study the general properties of the essential spectra of such operators. We then use this approach to investigate, and in some cases completely describe, the essential spectra of weighted rotation operators in Banach spaces of measurable and analytic functions.

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Notes

  1. 1.

    We do not assume that \(\mathcal {A}\) is a commutative semigroup.

  2. 2.

    The definition of Riemann integrable function on a compact topological space endowed with a Borel measure can be found in [8, p.130].

  3. 3.

    The condition that G is Hausdorff is often included in the definition of the topological group.

  4. 4.

    We do not call \(\Omega \) rotation invariant because usually this term is reserved for domains invariant under all linear unitary transformations of \(\mathbb {C}^n\).

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Correspondence to Arkady Kitover.

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Dedicated to Eric Nordgren and to the memory of Herbert Kamowitz.

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Kitover, A., Orhon, M. Spectrum of weighted composition operators part V spectrum and essential spectra of weighted rotation-like operators. Positivity 24, 973–1015 (2020). https://doi.org/10.1007/s11117-019-00714-z

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Keywords

  • Weighted rotation-like operators
  • Spectrum
  • Fredholm spectrum
  • Essential spectra

Mathematics Subject Classification

  • Primary 47B33
  • Secondary 47B48
  • 46B60