Constructing separated sequences in Banach spaces

Prus, Stanisław

doi:10.1090/S0002-9939-09-10024-2

Constructing separated sequences in Banach spaces
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Proc. Amer. Math. Soc. 138 (2010), 225-234 Request permission

Abstract:

A construction of separated sequences in the unit sphere of a Banach space is given. If a space $X$ admits an equivalent nearly uniformly convex norm or $c_0$ is not finitely representable in $X$, then lower bounds for separation constants of sequences are strictly greater than 1. This gives a partial answer to a problem posed by J. Diestel.

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