- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 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.2016.53.1.119Printed 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 Downloads: Full-text PDF