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An extension property for banach spaces

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A Banach space X has property (E) if every operator from X into c0 extends to an operator from X** into c0; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space. © 2002, Instytut Matematyczny. All rights reserved.

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Institute of Mathematics, Polish Academy of Sciences

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Mathematics

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Colloquium Mathematicum

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10.4064/cm91-2-2

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