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The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.

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The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces. / Laustsen, Niels Jakob; Loy, Richard J.; Read, Charles J.

In: Journal of Functional Analysis, Vol. 214, No. 1, 01.09.2004, p. 106-131.

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Laustsen, Niels Jakob ; Loy, Richard J. ; Read, Charles J. / The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces. In: Journal of Functional Analysis. 2004 ; Vol. 214, No. 1. pp. 106-131.

Bibtex

@article{e976c6fcd0d549bfa7819f3ce4ddcbdb,
title = "The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.",
abstract = "Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,… .",
keywords = "Ideal lattice, operator, Banach space, Banach algebra",
author = "Laustsen, {Niels Jakob} and Loy, {Richard J.} and Read, {Charles J.}",
year = "2004",
month = sep,
day = "1",
doi = "10.1016/j.jfa.2004.02.009",
language = "English",
volume = "214",
pages = "106--131",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "1",

}

RIS

TY - JOUR

T1 - The lattice of closed ideals in the Banach algebra of operators on certain Banach spaces.

AU - Laustsen, Niels Jakob

AU - Loy, Richard J.

AU - Read, Charles J.

PY - 2004/9/1

Y1 - 2004/9/1

N2 - Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,… .

AB - Very few Banach spaces E are known for which the lattice of closed ideals in the Banach algebra of all (bounded, linear) operators on E is fully understood. Indeed, up to now the only such Banach spaces are, up to isomorphism, Hilbert spaces and the sequence spaces c0 and ℓp for 1p<∞. We add a new member to this family by showing that there are exactly four closed ideals in for the Banach space E(ℓ2n)c0, that is, E is the c0-direct sum of the finite-dimensional Hilbert spaces ℓ21,ℓ22,…,ℓ2n,… .

KW - Ideal lattice

KW - operator

KW - Banach space

KW - Banach algebra

U2 - 10.1016/j.jfa.2004.02.009

DO - 10.1016/j.jfa.2004.02.009

M3 - Journal article

VL - 214

SP - 106

EP - 131

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -