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  • 1211.2867

    Rights statement: 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

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

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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A reflexive Banach space whose algebra of operators is not a Grothendieck space. / Kania, Tomasz.
In: Journal of Mathematical Analysis and Applications, Vol. 401, No. 1, 01.05.2013, p. 242-243.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Kania, T 2013, 'A reflexive Banach space whose algebra of operators is not a Grothendieck space', Journal of Mathematical Analysis and Applications, vol. 401, no. 1, pp. 242-243. https://doi.org/10.1016/j.jmaa.2012.12.017

APA

Kania, T. (2013). A reflexive Banach space whose algebra of operators is not a Grothendieck space. Journal of Mathematical Analysis and Applications, 401(1), 242-243. https://doi.org/10.1016/j.jmaa.2012.12.017

Vancouver

Kania T. A reflexive Banach space whose algebra of operators is not a Grothendieck space. Journal of Mathematical Analysis and Applications. 2013 May 1;401(1):242-243. Epub 2012 Dec 13. doi: 10.1016/j.jmaa.2012.12.017

Author

Kania, Tomasz. / A reflexive Banach space whose algebra of operators is not a Grothendieck space. In: Journal of Mathematical Analysis and Applications. 2013 ; Vol. 401, No. 1. pp. 242-243.

Bibtex

@article{ce678870271e424ab28877a26af9fe0f,
title = "A reflexive Banach space whose algebra of operators is not a Grothendieck space",
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 onthe 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 themonograph of Diestel and Uhl which asks whether the space of operators on areflexive Banach space is Grothendieck. ",
keywords = "Grothendieck space, Space of bounded operators, Reflexive space, Banach space",
author = "Tomasz Kania",
note = "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",
year = "2013",
month = may,
day = "1",
doi = "10.1016/j.jmaa.2012.12.017",
language = "English",
volume = "401",
pages = "242--243",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - A reflexive Banach space whose algebra of operators is not a Grothendieck space

AU - Kania, Tomasz

N1 - 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

PY - 2013/5/1

Y1 - 2013/5/1

N2 - 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 onthe 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 themonograph of Diestel and Uhl which asks whether the space of operators on areflexive Banach space is Grothendieck.

AB - 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 onthe 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 themonograph of Diestel and Uhl which asks whether the space of operators on areflexive Banach space is Grothendieck.

KW - Grothendieck space

KW - Space of bounded operators

KW - Reflexive space

KW - Banach space

U2 - 10.1016/j.jmaa.2012.12.017

DO - 10.1016/j.jmaa.2012.12.017

M3 - Journal article

VL - 401

SP - 242

EP - 243

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -