Three kinds of numerical indices of a Banach space II

Published in: Quaestiones Mathematicae
Volume 39 , issue 2 , 2016 , pages: 153–166

DOI: 10.2989/16073606.2015.1068236

Author(s): Sung Guen Kim Department of Mathematics, Republic of Korea

Keywords: Primary 46A22 , 46G20; Secondary 46G25 , Primary 46A22 , 46G20; Secondary 46G25

For a Banach space E and a positive integer k, we study about three kinds of numerical indices of E, the multilinear numerical index

(E), the symmetric multilinear numerical index

(E) and the polynomial numerical index

(E). First we show that

(E**) ≤

(E) for I=m, s and present some inequalities among

(E),

(E) and

(E). We also prove that if E is a strictly convex Banach space, then

(E)=0 for every k ≥ 2.

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