The Weak differentiability of norm and a generalized Bhatia-Šemrl Theorem

2022/02/25 by Roy, Saikat · 2 citations
#15A69 #46A32 #46G25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2202.12647

Abstract

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-Šemrl theorem on Birkhoff-James orthogonality.

Cited by

• Smoothness in the space of bounded linear operators on semi-Hilbert space
• Distance and best approximations in operator norm and trace class norm

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