Smoothness and estimates of sequences in Banach spaces
An upper bound for the order of smoothness of bump functions in Banach spaces without copy ofc 0 is found in terms of lower and upper estimates of their sequences. It is also shown that everyC ∞-smooth Banach space with symmetric basis either containsc 0 or is isomorphic toℓ 2n for some integern.
KeywordsBanach Space Orlicz Space Smooth Banach Space Spreading Model Unconditional Basis
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