Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices

Jaegil Kim, Han Ju Lee

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra A of Cb (K) is dense if and only if the set of all strong peak points is a norming subset of A. As a corollary we can induce the denseness of strong peak functions on other certain spaces. In case that a set of uniformly strongly exposed points of a Banach space X is a norming subset of P (nX), then the set of all strongly norm attaining elements in P (nX) is dense. In particular, the set of all points at which the norm of P (nX) is Fréchet differentiable is a dense Gδ subset. In the last part, using Reisner's graph-theoretic approach, we construct some strongly norm attaining polynomials on a CL-space with an absolute norm. Then we show that for a finite dimensional complex Banach space X with an absolute norm, its polynomial numerical indices are one if and only if X is isometric to ℓn. Moreover, we give a characterization of the set of all complex extreme points of the unit ball of a CL-space with an absolute norm.

Original languageEnglish
Pages (from-to)931-947
Number of pages17
JournalJournal of Functional Analysis
Volume257
Issue number4
DOIs
StatePublished - 15 Aug 2009

Keywords

  • Peak functions
  • Peak points
  • Polynomial numerical index

Fingerprint

Dive into the research topics of 'Strong peak points and strongly norm attaining points with applications to denseness and polynomial numerical indices'. Together they form a unique fingerprint.

Cite this