Original Research Article
Year: 2017 | Month: June | Volume: 4 | Issue: 6 | Pages: 31-43
The Strongly Compact Algebras
Osman Abdalla Adam Osman1,Yagoub Hussein Ahmed. H2
1Department of Mathematics - College of Science & Arts in Uglat Asugour - Qassim University - Saudi Arabia
2Department of Mathematics- College of Science -University of Sudan
Corresponding Author: Osman Abdalla Adam Osman
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.
Key words: strongly compact, Hilbert space, operators, subalgebra, relatively, commutant, topology.
[PDF Full Text]