COMPLETELY CONTINUOUS SUBSPACES OF OPERATOR IDEALS
Ülger, Saksman and Tylli have shown that if $X$ is a reflexive Banach space and $\mathcal{A}$ is a subalgebra of $K(X)$ such that $\mathcal{A}^*$ has the Schur property, then $\mathcal{A}$ is completely continuous. Here by introducing the concept of a strongly completely continuous subspace of an op...
| Published in: | Taiwanese Journal of Mathematics |
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| Main Authors: | , |
| Format: | Text |
| Language: | English |
| Published: |
Mathematical Society of the Republic of China
2006
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| Subjects: | |
| Online Access: | http://projecteuclid.org/euclid.twjm/1500403855 https://doi.org/10.11650/twjm/1500403855 |
| Summary: | Ülger, Saksman and Tylli have shown that if $X$ is a reflexive Banach space and $\mathcal{A}$ is a subalgebra of $K(X)$ such that $\mathcal{A}^*$ has the Schur property, then $\mathcal{A}$ is completely continuous. Here by introducing the concept of a strongly completely continuous subspace of an operator ideal, we improve their results. In particular, when $X$ is an $l_p$- direct sum and $Y$ is an $l_q$- direct sum of finite-dimensional Banach spaces with $1 \lt p \leq q \lt \infty$, we give a characterization of Schur property of the dual $\mathcal{M}^*$ of a closed subspace $\mathcal{M} \subseteq K(X,Y)$ in terms of strong complete continuity of $\mathcal{M}$. |
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