Differentiability of the norm in von Neumann algebras
HTML articles powered by AMS MathViewer
- by Keith F. Taylor and Wend Werner PDF
- Proc. Amer. Math. Soc. 119 (1993), 475-480 Request permission
Abstract:
Smooth points in von Neumann algebras are characterized in terms of minimal projections. The theorem generalizes known results for the algebra ${L^\infty }(\Omega ,\Sigma ,\mu )$ and the space of bounded linear operators on a Hilbert space.References
- Charles A. Akemann and Gert K. Pedersen, Facial structure in operator algebra theory, Proc. London Math. Soc. (3) 64 (1992), no. 2, 418–448. MR 1143231, DOI 10.1112/plms/s3-64.2.418
- C. M. Edwards and G. T. Rüttimann, On the facial structure of the unit balls in a $\textrm {JBW}^*$-triple and its predual, J. London Math. Soc. (2) 38 (1988), no. 2, 317–332. MR 966303, DOI 10.1112/jlms/s2-38.2.317
- S. Heĭnrih, The differentiability of the norm in spaces of operators, Funkcional. Anal. i Priložen. 9 (1975), no. 4, 93–94 (Russian). MR 0390834 R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras. I, II, Academic Press, New York and London, 1983, 1986.
- Fuad Kittaneh and Rahman Younis, Smooth points of certain operator spaces, Integral Equations Operator Theory 13 (1990), no. 6, 849–855. MR 1073855, DOI 10.1007/BF01198920
- Robert R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Mathematics, vol. 1364, Springer-Verlag, Berlin, 1989. MR 984602, DOI 10.1007/BFb0089089
- Masamichi Takesaki, Theory of operator algebras. I, Springer-Verlag, New York-Heidelberg, 1979. MR 548728
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 475-480
- MSC: Primary 46L10; Secondary 46B07
- DOI: https://doi.org/10.1090/S0002-9939-1993-1149980-6
- MathSciNet review: 1149980