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SOME OBSERVATIONS ON THE NUMERICAL INDEX AND THE POLYNOMIAL NUMERICAL INDEX

  • Kim, Sun Kwang (Department of Mathematics Kyonggi University)
  • Received : 2015.01.02
  • Published : 2016.01.31

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

Acknowledgement

Supported by : Kyonggi University

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