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Some observations on the numerical index and the polynomial numerical index

Sun Kwang Kim
대한수학회 (The Korean Mathematical Society)|2016.01|대한수학회보 (Bulletin of the KMS)|제53권 제1호|pp. 119-126

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참고문헌

키워드

polynomialnumerical indexpolynomial numerical indexrenorming
주제분류수학

초록

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 $\alpha\in [0,1/18)$.

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 $\alpha\in [0,1/18)$.

참고문헌 (21)

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