## Taiwanese Journal of Mathematics

### COMPLETELY CONTINUOUS SUBSPACES OF OPERATOR IDEALS

#### Abstract

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 $\mathcal{M}$.

#### Article information

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

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500403855

Digital Object Identifier
doi:10.11650/twjm/1500403855

Mathematical Reviews number (MathSciNet)
MR2206322

Zentralblatt MATH identifier
1109.47063

#### Citation

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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