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On injective or dense-range operators leaving a given chain of subspaces invariant

Author: Bamdad R. Yahaghi
Journal: Proc. Amer. Math. Soc. 132 (2004), 1059-1066
MSC (2000): Primary 47A15, 47A46, 47D03
Published electronically: 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 $\mathcal {S}$ 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.

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Additional Information

Bamdad R. Yahaghi
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 3G3

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
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.
Dedicated: With gratitude, dedicated to H. Hajiabolhassan, I. Mirfazeli, and F. Nouri
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society