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Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations

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Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations. / Laustsen, Niels Jakob; Skillicorn, Richard.
In: Studia Mathematica, Vol. 236, 10.11.2016, p. 51-62.

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@article{546bb57ab02543dca22b05955828e6e5,
title = "Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations",
abstract = "Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence{0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product. ",
keywords = "Bounded operator, Read's Banach space, Banach algebra, short-exact sequence, strong splitting, discontinuous derivation",
author = "Laustsen, {Niels Jakob} and Richard Skillicorn",
year = "2016",
month = nov,
day = "10",
doi = "10.4064/sm8554-9-2016",
language = "English",
volume = "236",
pages = "51--62",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",

}

RIS

TY - JOUR

T1 - Extensions and the weak Calkin algebra of Read's Banach space admitting discontinuous derivations

AU - Laustsen, Niels Jakob

AU - Skillicorn, Richard

PY - 2016/11/10

Y1 - 2016/11/10

N2 - Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence{0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product.

AB - Read produced the first example of a Banach space E such that the associated Banach algebra B(E) of bounded operators admits a discontinuous derivation (J. London Math. Soc. 1989). We generalize Read's main theorem about B(E) from which he deduced this conclusion, as well as the key technical lemmas that his proof relied on, by constructing a strongly split-exact sequence{0}→W(E)→B(E)→l2~→{0}, W(E) where W(E) denotes the ideal of weakly compact operators on E, while l2~ is the unitization of the Hilbert space l2, endowed with the zero product.

KW - Bounded operator

KW - Read's Banach space

KW - Banach algebra

KW - short-exact sequence

KW - strong splitting

KW - discontinuous derivation

U2 - 10.4064/sm8554-9-2016

DO - 10.4064/sm8554-9-2016

M3 - Journal article

VL - 236

SP - 51

EP - 62

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

ER -