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An image problem for compact operators

Authors: Isabelle Chalendar and Jonathan R. Partington
Journal: Proc. Amer. Math. Soc. 134 (2006), 1391-1396
MSC (2000): Primary 47A15, 47A46, 47B07
Published electronically: October 7, 2005
MathSciNet review: 2199185
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Abstract: Let $ \mathcal{X}$ be a separable Banach space and $ (\mathcal{X}_n)_n$ a sequence of closed subspaces of $ \mathcal{X}$ satisfying $ \mathcal{X}_n\subset \mathcal{X}_{n+1}$ for all $ n$. We first prove the existence of a dense-range and injective compact operator $ K$ such that each $ K\mathcal{X}_n$ is a dense subset of $ \mathcal{X}_n$, solving a problem of Yahaghi (2004). Our second main result concerns isomorphic and dense-range injective compact mappings between dense sets of linearly independent vectors, extending a result of Grivaux (2003).

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Additional Information

Isabelle Chalendar
Affiliation: Institut Girard Desargues, UFR de Mathématiques, Université Claude Bernard Lyon 1, 69622 Villeurbanne Cedex, France

Jonathan R. Partington
Affiliation: School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Keywords: Chains of invariant subspaces, compact operators, Banach spaces.
Received by editor(s): November 3, 2004
Received by editor(s) in revised form: December 9, 2004
Published electronically: October 7, 2005
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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