Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(1): 119-126

Printed January 31, 2016

https://doi.org/10.4134/BKMS.2016.53.1.119

Copyright © The Korean Mathematical Society.

Some observations on the numerical index and the polynomial numerical index

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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