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.
Mathematics Subject Classification (2000). Primary 47G30.
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Molahajloo, S. (2011). A Characterization of Compact Pseudo-Differential Operators on \(\mathbb{S}^1\) . In: Rodino, L., Wong, M., Zhu, H. (eds) Pseudo-Differential Operators: Analysis, Applications and Computations. Operator Theory: Advances and Applications(), vol 213. Springer, Basel. https://doi.org/10.1007/978-3-0348-0049-5_3
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DOI: https://doi.org/10.1007/978-3-0348-0049-5_3
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