Asymptotically isometric copies of c0 and l in certain Banach spaces |
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Authors: | Dongyang Chen |
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Institution: | Department of Mathematics, Nankai University, Tianjin 300071, China |
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Abstract: | If X is a separable Banach space, then X∗ contains an asymptotically isometric copy of l1 if and only if there exists a quotient space of X which is asymptotically isometric to c0. If X is an infinite-dimensional normed linear space and Y is any Banach space containing an asymptotically isometric copy of c0, then L(X,Y) contains an isometric copy of l∞. If X and Y are two infinite-dimensional Banach spaces and Y contains an asymptotically isometric copy of c0, then contains a complemented asymptotically isometric copy of c0. |
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