ESSENTIAL SPECTRA OF QUASI-PARABOLIC COMPOSITION OPERATORS ON HARDY SPACES OF THE POLY-DISC

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Gul U.

OPERATORS AND MATRICES, vol.7, no.4, pp.927-946, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 4
  • Publication Date: 2013
  • Doi Number: 10.7153/oam-07-52
  • Journal Name: OPERATORS AND MATRICES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.927-946
  • Hacettepe University Affiliated: Yes

Abstract

In this paper we study the essential spectra of a class of composition operators on the Hilbert-Hardy space of the hi-disc which is called "quasi-parabolic" and whose one variable analogue was studied in [2]. As in [2], quasi-parabolic composition operators on the Hilbert-Hardy space of the hi-disc are written as a linear combination of Toeplitz operators and Fourier multipliers. The C*-algebra generated by Toeplitz operators and Fourier multipliers on the Hilbert-Hardy space of the bi-disc is written as the tensor product of the similar C*-algebra in one variable with itself. As a result we find a nontrivial set consisting of spiral curves lying inside the essential spectra of quasi-parabolic composition operators.