Acta mathematica scientia,Series B
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Chen Dongyang
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Abstract:
Let X be a Banach space. If there exists a quotient space of X which is asymptotically isometric to l1, then X contains complemented asymptotically isometric copies of l1. Every infinite dimensional closed subspace of l1 contains a complemented subspace of l1 which is asymptotically isometric to l1. Let X be a separable Banach space such that X* contains asymptotically isometric copies of lp (1q (\frac{1}{p}+\frac{1}{q}=1). Complemented asymptotically isometric copies of c0 in K(X,Y) and W(X,Y) are discussed. Let X be a Gelfand-Phillips space. If X contains asymptotically isometric copies of c0, it has to contain complemented asymptotically isometric copies of c0.
Key words: Asymptotically isometric copies of, complemented asymptoticaly isometric copies of
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Chen Dongyang. ASYMPTOTICALLY ISOMETRIC COPIES OF lp (1≤ p<∞) AND c0 IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2006, 26(2): 281-290.
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URL: http://121.43.60.238/sxwlxbB/EN/10.1016/S0252-9602(06)60050-7
http://121.43.60.238/sxwlxbB/EN/Y2006/V26/I2/281
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