The Strongly Compact Algebras
Journal Title: International Journal of Research and Review - Year 2017, Vol 4, Issue 6
Abstract
Analgebra of bounded linear operators on a Hilbert space isstrongly compactif its unit ball is relatively compact in the strong operator topology. The algebra generated by the operator and the identity is strongly compact. This notion was introduced by Lomonosov as an approach to the invariant subspace problem for essentially normal operators. The basic properties of strongly compact algebras are established. A characterization of strongly compact normal operators is provided in terms of their spectral representation, and some applications. Finally, necessary and sufficient conditions for a weighted shift to be strongly compact are obtained in terms of the sliding products of its weights, and further applications are derived.
Authors and Affiliations
Osman Abdalla A. OS
Keywords
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