On the commutant and orbits of conjugation

Drissi, D.; Mbekhta, M.

doi:10.1090/S0002-9939-05-08047-0

On the commutant and orbits of conjugation
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Proc. Amer. Math. Soc. 134 (2006), 1099-1106 Request permission

Abstract:

In this note, we analyse the relationship between the commutant of a bounded linear operator $A$ and the algebra of similarity $B_A$ 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 Colojoarǎ-Foiaş 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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