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A Characterization of Compact Pseudo-Differential Operators on \(\mathbb{S}^1\)

  • Shahla MolahajlooEmail author
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 213)

Abstract

We first prove that a pseudo-differential operator of symbol of order 0 is essentially normal. Then by using Gohber’s lemma and a result from [6], a necessary and sufficient condition for compactness of pseudo-differential operators on the unit circle is given.

Keywords

Pseudo-differential operators compact operators Calkin algebra Fredholmness essential spectra 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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