International Journal of Nonlinear Analysis and Applications

Anti-N-order polynomial Daugavet property on Banach spaces

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, Mbarara University of Science and Technology, Uganda

Abstract

We generalize the notion of the anti-Daugavet property (a-DP) to the anti-N-order polynomial Daugavet property (a-NPDP) for Banach spaces by identifying a good spectrum of a polynomial and prove that locally uniformly alternatively convex or smooth Banach spaces have the a-mDP for rank-1 polynomials. We then prove that locally uniformly convex Banach spaces have the a-NPDP for compact polynomials if and only if their norms are eigenvalues, and uniformly convex Banach spaces have the a-NPDP for continuous polynomials if and only if their norms
belong to the approximate spectra.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 1
May 2021
Pages 1097-1105
  • Receive Date: 31 October 2018
  • Revise Date: 15 November 2019
  • Accept Date: 22 November 2019