Essential Spectra Of Quasi-Parabolic Composition Operators On Hardy Spaces Of The Poly-Disc
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.
