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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the commutant and orbits of conjugation


Authors: D. Drissi and M. Mbekhta
Journal: Proc. Amer. Math. Soc. 134 (2006), 1099-1106
MSC (2000): Primary 47B10, 47B15
Published electronically: July 25, 2005
MathSciNet review: 2196043
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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 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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Additional Information

D. Drissi
Affiliation: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Email: drissi@mcs.sci.kuniv.edu.kw

M. Mbekhta
Affiliation: UFR de Mathématiques, Université des Sciences et Technologie Lille, Villeneuve d’Asq, France
Email: Mostafa.Mbekhta@math.univ-lille1.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08047-0
PII: S 0002-9939(05)08047-0
Keywords: Commutant, bounded orbit, spectrum, generalized inverse
Received by editor(s): October 14, 2004
Received by editor(s) in revised form: November 1, 2004
Published electronically: July 25, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.