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On injective or dense-range operators leaving a given chain of subspaces invariant
Author(s):
Bamdad
R.
Yahaghi
Journal:
Proc. Amer. Math. Soc.
132
(2004),
1059-1066.
MSC (2000):
Primary 47A15, 47A46, 47D03
Posted:
July 14, 2003
MathSciNet review:
2045421
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Abstract:
In this paper we prove the existence of dense-range or one-to-one compact operators on a separable Banach space leaving a given finite chain of subspaces invariant. We use this result to prove that a semigroup  of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator  such that the collection  of compact operators is reducible.
References:
-
- [C]
- J. B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, 1990. MR 91e:46001
- [M]
- R. E. Megginson, An Introduction to Banach Space Theory, Springer-Verlag, New York, 1998. MR 99k:46002
- [RR]
- H. Radjavi and P. Rosenthal, Simultaneous Triangularization, Springer-Verlag, New York, 2000. MR 2001e:47001
- [Y1]
- B. R. Yahaghi, Near triangularizability implies triangularizability, to appear in the Canadian Mathematical Bulletin.
- [Y2]
- B. R. Yahaghi, Reducibility Results on Operator Semigroups, Ph.D. Thesis, Dalhousie University, Halifax, Canada, 2002.
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Additional Information:
Bamdad
R.
Yahaghi
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3
Email:
bamdad5@math.toronto.edu, reza5@mscs.dal.ca
DOI:
10.1090/S0002-9939-03-07139-9
PII:
S 0002-9939(03)07139-9
Keywords:
Linear functional,
invariant subspace,
reducible,
weak* topology
Received by editor(s):
October 15, 2002
Received by editor(s) in revised form:
November 16, 2002
Posted:
July 14, 2003
Additional Notes:
The author gratefully acknowledges the support of an Izaak Walton Killam Memorial Scholarship at Dalhousie University as well as an NSERC PDF at the University of Toronto.
Dedicated:
With gratitude, dedicated to H. Hajiabolhassan, I. Mirfazeli, and F. Nouri
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2003,
American Mathematical Society
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