Two sided ideals of operators : Notas de Matemática, 5

Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for inst- ance, when X = l<SUP>p</...

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Autor principal: Porta, Horacio
Formato: Publicacion seriada
Lenguaje:Inglés
Publicado: 1968
Materias:
Matemática
Espacios de Banach
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/159179
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SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-159179
record_format dspace
spelling I19-R120-10915-1591792024-05-09T14:05:46Z http://sedici.unlp.edu.ar/handle/10915/159179 Two sided ideals of operators : Notas de Matemática, 5 Porta, Horacio 1968-09 2023-10-20T17:35:20Z en Matemática Espacios de Banach Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for inst- ance, when X = l<SUP>p</SUP>, l ≦ p < ∞, L(X) is a chain (i.e., totally ordered) with three elements: (0), B(X) and the ideal C(X) of compact operators (see (3)). On the other hand, it is known ((2), 5.23) that for X = L<SUP>p</SUP>, 1 < p < ∞, the lattice L(X) is not a chain. A treatment for X a Hilbert space of arbitrary dimensión can be found in (4). We aim to exhibit here a Banach space X such that L(X) is both "long" and "wide". Material digitalizado en SEDICI gracias a la colaboración de la Biblioteca del Departamento de Matemática de la Facultad de Ciencias Exactas (UNLP). Facultad de Ciencias Exactas Publicacion seriada Publicacion seriada http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) application/pdf
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Espacios de Banach
spellingShingle Matemática
Espacios de Banach
Porta, Horacio
Two sided ideals of operators : Notas de Matemática, 5
topic_facet Matemática
Espacios de Banach
description Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for inst- ance, when X = l<SUP>p</SUP>, l ≦ p < ∞, L(X) is a chain (i.e., totally ordered) with three elements: (0), B(X) and the ideal C(X) of compact operators (see (3)). On the other hand, it is known ((2), 5.23) that for X = L<SUP>p</SUP>, 1 < p < ∞, the lattice L(X) is not a chain. A treatment for X a Hilbert space of arbitrary dimensión can be found in (4). We aim to exhibit here a Banach space X such that L(X) is both "long" and "wide".
format Publicacion seriada
Publicacion seriada
author Porta, Horacio
author_facet Porta, Horacio
author_sort Porta, Horacio
title Two sided ideals of operators : Notas de Matemática, 5
title_short Two sided ideals of operators : Notas de Matemática, 5
title_full Two sided ideals of operators : Notas de Matemática, 5
title_fullStr Two sided ideals of operators : Notas de Matemática, 5
title_full_unstemmed Two sided ideals of operators : Notas de Matemática, 5
title_sort two sided ideals of operators : notas de matemática, 5
publishDate 1968
url http://sedici.unlp.edu.ar/handle/10915/159179
work_keys_str_mv AT portahoracio twosidedidealsofoperatorsnotasdematematica5
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