Strongly closed bounded Boolean algebras of projections
Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 73-75
Voir la notice de l'article provenant de la source Cambridge University Press
It is known that every complete Boolean algebra of projections on a Banach space X is strongly closed and bounded and that, although the converse of this result fails in general, it is valid if X is weakly sequentially complete [1, XVII. 3, pp. 2194–2201]. In the present note it is shown that this converse is in fact valid precisely when X contains no subspace isomorphics to the sequence space c0. More explicitly, the following two results are proved. In both, X may be a real or complex space, but c0 will consist of the null sequences in the underlying scalar field.
Gillespie, T. A. Strongly closed bounded Boolean algebras of projections. Glasgow mathematical journal, Tome 22 (1981) no. 1, pp. 73-75. doi: 10.1017/S0017089500004481
@article{10_1017_S0017089500004481,
author = {Gillespie, T. A.},
title = {Strongly closed bounded {Boolean} algebras of projections},
journal = {Glasgow mathematical journal},
pages = {73--75},
year = {1981},
volume = {22},
number = {1},
doi = {10.1017/S0017089500004481},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004481/}
}
TY - JOUR AU - Gillespie, T. A. TI - Strongly closed bounded Boolean algebras of projections JO - Glasgow mathematical journal PY - 1981 SP - 73 EP - 75 VL - 22 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500004481/ DO - 10.1017/S0017089500004481 ID - 10_1017_S0017089500004481 ER -
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