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

Gul U.

OPERATORS AND MATRICES, cilt.7, ss.927-946, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 7 Konu: 4
  • Basım Tarihi: 2013
  • Doi Numarası: 10.7153/oam-07-52
  • Dergi Adı: OPERATORS AND MATRICES
  • Sayfa Sayıları: ss.927-946

Özet

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.