A note on operator Banach spaces containing a complemented copy of c0 |
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Authors: | F Paneque C Piñeiro |
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Institution: | Departamento de Matemáticas, Escuela Politécnica Superior, Universidad de Huelva, 21810 La Rábida, Huelva, Spain, ES
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Abstract: | Let X and Y Banach spaces. Two new properties of operator Banach spaces are introduced. We call these properties "boundedly closed" and "d-boundedly closed". Among other results, we prove the following one. Let U(X, Y){\cal U}(X, Y) an operator Banach space containing a complemented copy of c0. Then we have: 1) If U(X, Y){\cal U}(X, Y) is boundedly closed then Y contains a copy of c0. 2) If U(X, Y){\cal U}(X, Y) is d-boundedly closed, then X* or Y contains a copy of c0. |
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