A numerical range characterization of uniformly smooth Banach spaces

Palacios, Angel

doi:10.1090/S0002-9939-00-05621-5

A numerical range characterization of uniformly smooth Banach spaces
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by Angel Rodriguez Palacios PDF

Proc. Amer. Math. Soc. 129 (2001), 815-821 Request permission

Abstract:

We prove that a Banach space $X$ is uniformly smooth if and only if, for every $X$-valued bounded function $f$ on the unit sphere of $X$, the intrinsic numerical range of $f$ is equal to the closed convex hull of the spatial numerical range of $f$.

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