Differentiability of the Norm in Von Neumann Algebras

Abstract

Abstract. Smooth points in von Neumann algebras are characterized in terms of minimal projections. The theorem generalizes known results for the algebra L°°(Q, I, n) and the space of bounded linear operators on a Hilbert space.

C*-Algebras That AreI-Rings

“…tiability of the norm of C*-algebras in algebraic terms Theorem 1 . This latter result parallels similar characterizations of points of Frechetw x differentiability, which had been obtained in 21,22 . Nevertheless, in the framework of C*-algebras, strongly subdifferentiability of the norm happens to be much weaker than Frechet-differentiability.…”

Subdifferentiability of the norm and the Banach-Stone theorem for real and complex JB*-triples

“…By [24,Theorem] we conclude that C(Ω 1 , C) (and hence C(Ω 1 , R)) is Frechetsmooth at x 1 or C(Ω 2 , C) (and hence C(Ω 2 , C) R ) is Frechet-smooth at x 2 . It can be easily seen that C is Frechet-smooth at x.…”

Smoothness Properties of the Unit Ball in a JB* -Triple

“…A smooth point a is said to be Fre'chet-smooth if, for each sequence (x n ) in V* such that the sequence (x n (a)) converges to one, it follows that (jc n ) converges in norm to x. For the equivalence of these definitions with the conventional ones, the reader is referred to [18] and [19].…”