English

Locally octahedral and locally almost square K\"othe-Bochner spaces

Functional Analysis 2021-07-05 v1

Abstract

It has been proved in [J.-D. Hardtke, J. Math. Phys. Anal. Geom. 16, no.2, 119--137 (2020)] that a K\"othe-Bochner space E(X)E(X) is locally octahedral/locally almost square if XX has the respective property and the simple functions are dense in E(X)E(X). Here we show that the result still holds true without the density assumption. The proof makes use of the Kuratowski-Ryll-Nardzewski Theorem on measurable selections.

Keywords

Cite

@article{arxiv.2107.01180,
  title  = {Locally octahedral and locally almost square K\"othe-Bochner spaces},
  author = {Jan-David Hardtke},
  journal= {arXiv preprint arXiv:2107.01180},
  year   = {2021}
}

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6 pages