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Elements with generalized bounded conjugation orbits
Author(s):
Driss
Drissi;
Mostafa
Mbekhta
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2011-2016.
MSC (2000):
Primary 47B10, 47B15
Posted:
January 17, 2001
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Abstract:
For a pair of linear bounded operators  and  on a complex Banach space  , if  commutes with  then the orbits  of  under  are uniformly bounded. The study of the converse implication was started in the 1970s by J. A. Deddens. In this paper, we present a new approach to this type of question using two localization theorems; one is an operator version of a theorem of tauberian type given by Katznelson-Tzafriri and the second one is on power-bounded operators by Gelfand-Hille. This improves former results of Deddens-Stampfli-Williams.
References:
- [1]
- B. Aupetit and D. Drissi: Some spectral inequalities involving generalized scalar operators, Studia Math. 109 (1994), 51-66. MR 95b:47041
- [2]
- T. Bermudez, M. Gonzalez and M. Mbekhta: Local ergodic theorems, Extracta Math. 13(1997),243-248. MR 99k:47018
- [3]
- J. A. Deddens and T. K. Wong: The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc., 184(1973), 261-273. MR 48:2819
- [4]
- J. A. Deddens: Another description of nest algebras in Hilbert spaces operators, Lecture notes in Mathematics No. 693, (pp. 77-86), Springler-Verlag, Berlin, 1978. MR 80f:47033
- [5]
- R. deLaubenfels and P. Q. Vu: The discrete Hille-Yoshida space and the asymptotic behaviour of individual orbits of linear operators, J. Funct. Anal. 142(1996), 539-548. MR 98h:47059
- [6]
- D. Drissi and M. Mbekhta: Operators with bounded conjugation orbits, Proc. Amer. Math. Soc. 128(2000), 2687-2691. CMP 2000:14
- [7]
- P. R. Halmos: A Hilbert Space Problem Book, Von Nostrand, Princeton, 1967. MR 34:8178
- [8]
- G. Lumer and M. Rosenblum: Linear operators equations, Proc. Amer. Math. Soc. 10(1959), 32-41. MR 21:2927
- [9]
- M. Radjabalipour: Operators commuting with positive operators, Proc. Amer. Math. Soc. 77(1979), 107-110. MR 81d:47013
- [10]
- P. G. Roth: Bounded orbits of conjugation, analytic theory, Indiana Univ. Math. J, 32 (1983), 491-509. MR 85c:47039
- [11]
- G. E. Shilov: On a theorem of I.M. Gel'fand and its generalizations, Dokl. Akad. Nauk SSSR 72(1950), 641-644.
- [12]
- J. G. Stampfli: On a question of Deddens in Hilbert space operators, Lecture Notes in Mathematics No. 693, (pp. 169-173), Springer-Verlag, Berlin, 1978. MR 80f:47034
- [13]
- J. P. Williams: On a boundedness condition for operators with singleton spectrum, Proc. Amer. Math. Soc. 78(1980), 30-32. MR 81k:47008
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Additional Information:
Driss
Drissi
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
Email:
drissi@mcs.sci.kuniv.edu.kw
Mostafa
Mbekhta
Affiliation:
UMR-CNRS 8524 & UFR de Mathematiques, Université de Lille I, F-59655, Villeneuve d'asq, France
Email:
Mostafa.Mbekhta@univ-lille1.fr
DOI:
10.1090/S0002-9939-01-05945-7
PII:
S 0002-9939(01)05945-7
Keywords:
Bounded conjugation orbit,
spectrum,
spectral radius
Received by editor(s):
November 1, 1999
Posted:
January 17, 2001
Additional Notes:
Research of the first author partially supported by grants from Kuwait University.
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2001,
American Mathematical Society
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