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On the commutant and orbits of conjugation
Author(s):
D.
Drissi;
M.
Mbekhta
Journal:
Proc. Amer. Math. Soc.
134
(2006),
1099-1106.
MSC (2000):
Primary 47B10, 47B15
Posted:
July 25, 2005
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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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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:
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
Posted:
July 25, 2005
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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