Some observations on the numerical index and the polynomial numerical index
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 119-126
https://doi.org/10.4134/BKMS.2016.53.1.119
Printed January 31, 2016
Sun Kwang Kim
Kyonggi University
Abstract : In this paper, we study both the numerical index and the polynomial numerical index. First, we give a sufficient condition for a Banach space $X$ to have lushness. Second, we study the relation between the renormings of a Banach space and the $k$-order polynomial numerical index. This shows that every real Banach spaces of dimension greater that 1 can be renormed to have 2-order polynomial numerical index $\alpha$ for any $\alpha\in [0,1/18)$.
Keywords : numerical index, polynomial numerical index, polynomial, renorming
MSC numbers : Primary 46B04; Secondary 46G25, 46E30, 47A12, 47H60
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