1. Finitely strictly singular operators between James spaces
- Author
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Chalendar, Isabelle, Fricain, Emmanuel, Popov, Alexey I., Timotin, Dan, and Troitsky, Vladimir G.
- Subjects
- *
BANACH spaces , *OPERATOR algebras , *INVARIANT subspaces , *GENERALIZED spaces , *MATHEMATICAL singularities - Abstract
Abstract: An operator between Banach spaces is said to be finitely strictly singular if for every there exists n such that every subspace with contains a vector x such that . We show that, for , the formal inclusion operator from to is finitely strictly singular. As a consequence, we obtain that the strictly singular operator with no invariant subspaces constructed by C. Read is actually finitely strictly singular. These results are deduced from the following fact: if then every k-dimensional subspace of contains a vector x with such that for some . [Copyright &y& Elsevier]
- Published
- 2009
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