Abstract
Using the notion of thin sets we prove a theorem of Weyl type for the Wolf essential spectrum ofT ∈β (H). *Further we show that Weyl’s theorem holds for a restriction convexoid operator and consequently modify some results of Berberian. Finally we show that Weyl’s theorem holds for a paranormal operator and that a polynomially compact paranormal operator is a compact perturbation of a diagnoal normal operator. A structure theorem for polynomially compact paranormal operators is also given.
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Prasanna, S. Weyl’s theorem and thin spectra. Proc. Indian Acad. Sci. (Math. Sci.) 91, 59–63 (1982). https://doi.org/10.1007/BF02837261
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DOI: https://doi.org/10.1007/BF02837261