Approximate Birkhoff-James orthogonality preserver on Lebesgue-Bochner spaces

Abstract

In this article, we examine an approximate version of Koldobsky-Blanco-TurnÅ¡ek theorem (namely, Property P) in the space of vector-valued integrable functions. More precisely, we prove that the Lebesgue-Bochner spaces $L^p(\hat{I}¼,X),(1\le p<\infty )$, do not have Property P under certain conditions on $\hat{I}¼$ and the Banach space $X$.

11 pages