Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of the Poly-disc

Details Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of the Poly-disc Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of the Poly-disc

2012-01-04

arxiv.org/abs/1201.0839v1

Mathematics

Functional Analysis

Scientific paper

This work is a generalization of the results in [Gul] to bi-disc case. As in [Gul], quasi-parabolic composition operators on the Hilbert-Hardy space of the bi-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 lying inside the essential spectra of quasi-parabolic composition operators.

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