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Asymptotically Isometric Copies ofc0in Banach Spaces

✍ Scribed by P.N Dowling; C.J Lennard; B Turett

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 189 KB
Volume: 219
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5820

No coin nor oath required. For personal study only.

✦ Synopsis

If ⌫ is an uncountable set, then any equivalent renorming of c ⌫ contains an 0 asymptotically isometric copy of c . If Y is an infinite dimensional closed subspace 0 Ž 5 5 . of c и , then Y contains an asymptotically isometric copy of c . If X and Y are ϱ 0 0 two infinite dimensional Banach spaces and if X contains an asymptotically îsometric copy of c , then the injective tensor product of X and Y, X m Y, 0 contains a complemented asymptotically isometric copy of c . Similarly, if X 0 contains an asymptotically isometric copy of c , then the Lebesgue᎐Bochner 0 p Žw x . space L 0, 1 , X contains a complemented asymptotically isometric copy of c . 0

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