On the commutant and orbits of conjugation |
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Authors: | D Drissi M Mbekhta |
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Institution: | Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait ; UFR de Mathématiques, Université des Sciences et Technologie Lille, Villeneuve d'Asq, France |
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Abstract: | In this note, we analyse the relationship between the commutant of a bounded linear operator and the algebra of similarity that was introduced in the late 70s as a characterization of nest algebras. Necessary and sufficient conditions are also obtained for an operator to commute with real scalar generalized operators in the sense of Colojoara-Foias in Banach spaces. In the second part, we analyse the relationship between the generalized inverse, the generalized commutant and the orbits of conjugation. |
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Keywords: | Commutant bounded orbit spectrum generalized inverse |
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