Numerical index and renorming

Finet, Catherine; Martín, Miguel; Payá, Rafael

doi:10.1090/S0002-9939-02-06576-0

Numerical index and renorming
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by Catherine Finet, Miguel Martín and Rafael Payá PDF

Proc. Amer. Math. Soc. 131 (2003), 871-877 Request permission

Abstract:

We study the numerical index of a Banach space from the isomorphic point of view, that is, we investigate the values of the numerical index which can be obtained by renorming the space. The set of these values is always an interval which contains $[0,1/3[$ in the real case and $[e^{-1},1/2[$ in the complex case. Moreover, for “most” Banach spaces the least upper bound of this interval is as large as possible, namely $1$.

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