Restrictions of bounded linear operators: Closed range
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- by Bruce A. Barnes PDF
- Proc. Amer. Math. Soc. 135 (2007), 1735-1740 Request permission
Abstract:
Let $T$ be a bounded linear operator on a Banach space $X,$ and let $W$ be a subspace of $X$ which is a Banach space and $T-$ invariant. Denote by $T_{W}$ the restriction of $T$ to $W.$ This paper explores the questions: $\circ$ If the range of $T$ is closed, under what conditions is the range of $T_{W}$ closed? $\circ$ If the range of $T_{W}$ is closed, under what conditions is the range of $T$ closed?References
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Additional Information
- Bruce A. Barnes
- Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
- Email: barnes@uoregon.edu
- Received by editor(s): September 9, 2005
- Received by editor(s) in revised form: December 28, 2005
- Published electronically: November 15, 2006
- Communicated by: Joseph A. Ball
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 1735-1740
- MSC (2000): Primary 47A05
- DOI: https://doi.org/10.1090/S0002-9939-06-08624-2
- MathSciNet review: 2286083