The Weak differentiability of norm and a generalized Bhatia-Semrl Theorem
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-Semrl theorem on Birkhoff-James orthogonality.
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