Souvik Ghosh

On the simultaneous zero inclusion property and characterization of Inner product space

We show that if a Banach space $X$ is smooth and almost locally uniformly rotund and if satisfies the following \[0\in W(T) \implies 0\in W(T^{-1})\] for all invertible bounded linear map on $X$ then Birkhoff-James orthogonality in $X$ is symmetric. This result, therefore, characterizes the inner product spaces out of...