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Isometric Copies of c0 and ℓ∞ in Duals of Banach Spaces

✍ Scribed by Patrick N. Dowling

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
63 KB
Volume
244
Category
Article
ISSN
0022-247X

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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 a

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Let X be a Banach space and µ be a finite measure space. It is shown that if 1 ≤ p < ∞ resp 1 < p < ∞ , the Bochner space L p µ X contains asymptotically isometric copies of c 0 resp l 1 if and only if X does.