Generalized inverses in C*-algebras II

Harte, Robin; Мbekhta, Mostafa

doi:10.4064/sm-106-2-129-138

Cited by 66 publications

(53 citation statements)

References 8 publications

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“…Si A est une C n -alge`bre et a 2 A; notons par L a : A ! A l'ope´rateur de multiplication a`gauche, de´fini par L a x ¼ ax si x 2 A: Alors la conorme de a 2 A sera par de´finition gðaÞ :¼ gðL a Þ: Dans [9,10,18], on trouve les re´sultats suivants, si a 2 A alors…”

Section: Formules De Distance Au Spectre Semi-fredholmunclassified

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Formules de distance au spectre généralisé et au spectre semi-Fredholm

Мbekhta¹

2002

Journal of Functional Analysis

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Section: Formules De Distance Au Spectre Semi-fredholmunclassified

“…Notons que dans cette de´finition la premie`re e´galite´est ne´cessaire et suffisante pour que T admette un inverse ge´ne´ralise´(voir [5,9,10,17]). …”

Section: Introductionunclassified

Formules de distance au spectre généralisé et au spectre semi-Fredholm

Мbekhta¹

2002

Journal of Functional Analysis

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“…This definition is equivalent to the one introduced by Kato for operators in Banach spaces (see [9], Chapter IV). We recall here two important properties of γ(a) (see [8] and [12] for more details):…”

Section: Generalized Inverse and Orbits Of Conjugationmentioning

confidence: 99%

On the commutant and orbits of conjugation

Drissi

Мbekhta²

2005

Proc. Amer. Math. Soc.

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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. Introduction Let B(X), B(H)and A denote respectively the algebra of all bounded linear operators on a complex Banach space X, the algebra of all bounded linear operators on the complex separable infinite-dimensional Hilbert space H, and a complex Banach algebra. The symbols σ(S) and r(S) denote respectively the spectrum and the spectral radius of the operator S ∈ B(X), and as usual S is called quasinilpotent if σ(S) = {0}. Given an invertible operator A, the study of operators T whose conjugation orbit {A n T A −n } is bounded, that is, for T ∈ B(X) and A invertible, Recently, a quantitative version of these results was given in [6] (see also [7]). It provides us with a bound on e

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“…(see [13]- [14], [16], [21]). The set of all a ∈ A that possess the Moore-Penrose inverse will be denoted by A † .…”

Section: = a B C D mentioning

confidence: 99%