On injective or dense-range operators leaving a given chain of subspaces invariant
HTML articles powered by AMS MathViewer
- by Bamdad R. Yahaghi
- Proc. Amer. Math. Soc. 132 (2004), 1059-1066
- DOI: https://doi.org/10.1090/S0002-9939-03-07139-9
- Published electronically: July 14, 2003
- PDF | Request permission
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 $\mathcal {S}$ of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator $K$ such that the collection $\mathcal {S} K$ of compact operators is reducible.References
- John B. Conway, A course in functional analysis, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR 1070713
- Robert E. Megginson, An introduction to Banach space theory, Graduate Texts in Mathematics, vol. 183, Springer-Verlag, New York, 1998. MR 1650235, DOI 10.1007/978-1-4612-0603-3
- S. Losinsky, Sur le procédé d’interpolation de Fejér, C. R. (Doklady) Acad. Sci. URSS (N.S.) 24 (1939), 318–321 (French). MR 0002001
- B. R. Yahaghi, Near triangularizability implies triangularizability, to appear in the Canadian Mathematical Bulletin.
- B. R. Yahaghi, Reducibility Results on Operator Semigroups, Ph.D. Thesis, Dalhousie University, Halifax, Canada, 2002.
Bibliographic 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
- Received by editor(s): October 15, 2002
- Received by editor(s) in revised form: November 16, 2002
- Published electronically: 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.
- Communicated by: Joseph A. Ball
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 1059-1066
- MSC (2000): Primary 47A15, 47A46, 47D03
- DOI: https://doi.org/10.1090/S0002-9939-03-07139-9
- MathSciNet review: 2045421
Dedicated: With gratitude, dedicated to H. Hajiabolhassan, I. Mirfazeli, and F. Nouri