Denseness of Norm-Attaining Mappings on Banach Spaces

  • Yun Sung Choi

    Pohang University of Science and Technology, Pohang City, Kyungbuk, South Korea
  • Han Ju Lee

    Dongguk University, Seoul, South Korea
  • Hyun Gwi Song

    Sogang University, Seoul, South Korea

Abstract

Let and be Banach spaces. Let be the space of all -valued continuous -homogeneous polynomials on . We show that the set of all norm-attaining elements is dense in when a set of u.s.e. points of the unit ball is dense in the unit sphere . Applying strong peak points instead of u.s.e. points, we generalize this result to a closed subspace of , where is a complete metric space. For complex Banach spaces and , let be the Banach space of all bounded continuous -valued mappings on whose restrictions to the open unit ball are holomorphic. It follows that the set of all norm-attaining elements is dense in if the set of all strong peak points in is a norming subset for .

Cite this article

Yun Sung Choi, Han Ju Lee, Hyun Gwi Song, Denseness of Norm-Attaining Mappings on Banach Spaces. Publ. Res. Inst. Math. Sci. 46 (2010), no. 1, pp. 171–182

DOI 10.2977/PRIMS/4