A reflexive Banach space whose algebra of operators is not a Grothendieck space

Kania, Tomasz (2013) A reflexive Banach space whose algebra of operators is not a Grothendieck space. Journal of Mathematical Analysis and Applications, 401 (1). pp. 242-243. ISSN 0022-247X

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Abstract

By a result of Johnson, the Banach space $F=(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_\infty}$ contains a complemented copy of $\ell_1$. We identify $F$ with a complemented subspace of the space of (bounded, linear) operators on the reflexive space $(\bigoplus_{n=1}^\infty \ell_1^n)_{\ell_p}$ ($p\in (1,\infty))$, thus giving a negative answer to the problem posed in the monograph of Diestel and Uhl which asks whether the space of operators on a reflexive Banach space is Grothendieck.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Mathematical Analysis and Applications
Additional Information:
This is the pre-print version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, 401, 1, 2013 DOI: 10.1016/j.jmaa.2012.12.017
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2604
Subjects:
ID Code:
73759
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Deposited On:
18 Jun 2015 05:44
Refereed?:
Yes
Published?:
Published
Last Modified:
02 Aug 2020 03:08