Taiwanese Journal of Mathematics


S. M. Moshtaghioun and J. Zafarani

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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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Taiwanese J. Math., Volume 10, Number 3 (2006), 691-698.

First available in Project Euclid: 18 July 2017

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Zentralblatt MATH identifier

Primary: 47L05: Linear spaces of operators [See also 46A32 and 46B28] 47L20: Operator ideals [See also 47B10]
Secondary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46B99: None of the above, but in this section

Schur property completely continuous algebra compact operator operator ideal


Moshtaghioun, S. M.; Zafarani, J. COMPLETELY CONTINUOUS SUBSPACES OF OPERATOR IDEALS. Taiwanese J. Math. 10 (2006), no. 3, 691--698. doi:10.11650/twjm/1500403855. https://projecteuclid.org/euclid.twjm/1500403855

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