Some geometric properties of spaces of vector-valued integrable functions

Mohit; Ranjana Jain

Some geometric properties of spaces of vector-valued integrable functions

Functional Analysis 2025-04-07 v2

Authors: Mohit , Ranjana Jain

Abstract

We identify the smooth points of $L^1(\mu,X)$ , and provide some necessary and sufficient conditions for left and right symmetry of points with respect to Birkhoff-James orthogonality in $L^p(\mu,X), 1\leq p<\infty$ , where $\mu$ is any complete positive measure and $X$ is a Banach space with some suitable properties.

Keywords

Birkhoff-James orthogonality vector-valued integrable functions smooth points L¹ space Lᵖ space Banach space left and right symmetry

Cite

@article{arxiv.2411.03798,
  title  = {Some geometric properties of spaces of vector-valued integrable functions},
  author = {Mohit and Ranjana Jain},
  journal= {arXiv preprint arXiv:2411.03798},
  year   = {2025}
}

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