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  • KaniaLaustsenSkillicorn

    Rights statement: This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. 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 Functional Analysis, 271, 2016 DOI: 10.1016/j.jfa.2016.05.019

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A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

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

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A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. / Kania, Tomasz; Laustsen, Niels Jakob; Skillicorn, Richard.
In: Journal of Functional Analysis, Vol. 271, 20.09.2016, p. 2888-2898.

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

Harvard

Kania, T, Laustsen, NJ & Skillicorn, R 2016, 'A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space', Journal of Functional Analysis, vol. 271, pp. 2888-2898. https://doi.org/10.1016/j.jfa.2016.05.019

APA

Kania, T., Laustsen, N. J., & Skillicorn, R. (2016). A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. Journal of Functional Analysis, 271, 2888-2898. https://doi.org/10.1016/j.jfa.2016.05.019

Vancouver

Kania T, Laustsen NJ, Skillicorn R. A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. Journal of Functional Analysis. 2016 Sept 20;271:2888-2898. Epub 2016 Jun 2. doi: 10.1016/j.jfa.2016.05.019

Author

Kania, Tomasz ; Laustsen, Niels Jakob ; Skillicorn, Richard. / A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space. In: Journal of Functional Analysis. 2016 ; Vol. 271. pp. 2888-2898.

Bibtex

@article{d97f4c94df644f90ae78b472b8331854,
title = "A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space",
abstract = "Let E be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra B(E) of bounded operators on E admits a discontinuous derivation. We show that B(E) has a singular, admissible extension which splits algebraically, but does not split strongly. This answers anatural question going back to the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C.R. Math. Acad. Sci. Paris 2016).",
keywords = "Bounded, linear operator, Banach space, Banach algebra, short-exact sequence, algebraic splitting, strong splitting, singular extension, admissible extension, pullback, separating space",
author = "Tomasz Kania and Laustsen, {Niels Jakob} and Richard Skillicorn",
note = "This is the author{\textquoteright}s version of a work that was accepted for publication in Journal of Functional Analysis. 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 Functional Analysis, 271, 2016 DOI: 10.1016/j.jfa.2016.05.019",
year = "2016",
month = sep,
day = "20",
doi = "10.1016/j.jfa.2016.05.019",
language = "English",
volume = "271",
pages = "2888--2898",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - A singular, admissible extension which splits algebraically, but not strongly, of the algebra of bounded operators on a Banach space

AU - Kania, Tomasz

AU - Laustsen, Niels Jakob

AU - Skillicorn, Richard

N1 - This is the author’s version of a work that was accepted for publication in Journal of Functional Analysis. 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 Functional Analysis, 271, 2016 DOI: 10.1016/j.jfa.2016.05.019

PY - 2016/9/20

Y1 - 2016/9/20

N2 - Let E be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra B(E) of bounded operators on E admits a discontinuous derivation. We show that B(E) has a singular, admissible extension which splits algebraically, but does not split strongly. This answers anatural question going back to the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C.R. Math. Acad. Sci. Paris 2016).

AB - Let E be the Banach space constructed by Read (J. London Math. Soc. 1989) such that the Banach algebra B(E) of bounded operators on E admits a discontinuous derivation. We show that B(E) has a singular, admissible extension which splits algebraically, but does not split strongly. This answers anatural question going back to the work of Bade, Dales, and Lykova (Mem. Amer. Math. Soc. 1999), and complements recent results of Laustsen and Skillicorn (C.R. Math. Acad. Sci. Paris 2016).

KW - Bounded, linear operator

KW - Banach space

KW - Banach algebra

KW - short-exact sequence

KW - algebraic splitting

KW - strong splitting

KW - singular extension

KW - admissible extension

KW - pullback

KW - separating space

U2 - 10.1016/j.jfa.2016.05.019

DO - 10.1016/j.jfa.2016.05.019

M3 - Journal article

VL - 271

SP - 2888

EP - 2898

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

ER -