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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| Formato: | Publicacion seriada |
| Lenguaje: | Inglés |
| Publicado: |
1968
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/159179 |
| Aporte de: |
| Sumario: | 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". |
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