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.
Sun Kwang Kim
Kyonggi University
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
2021; 58(4): 939-958
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