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arXiv · 2601.02786

Approximate Birkhoff-James orthogonality preserver on Lebesgue-Bochner spaces

Mohit·Ranjana Jain
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Abstract

In this article, we examine an approximate version of Koldobsky-Blanco-Turn\v{s}ek theorem (namely, Property P) in the space of vector-valued integrable functions. More precisely, we prove that the Lebesgue-Bochner spaces $L^p(\mu,X),\;(1\leq p<\infty)$, do not have Property P under certain conditions on $\mu$ and the Banach space $X$.

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Mohit, Ranjana Jain. 2026-01-06. Approximate Birkhoff-James orthogonality preserver on Lebesgue-Bochner spaces. https://arxiv.org/abs/2601.02786

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