Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Differentiability of the norm in von Neumann algebras


Authors: Keith F. Taylor and Wend Werner
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] C. A. Akemann and G. K. Pedersen, Facial structure in operator algebra theory, Proc. London Math. Soc. 64 (1992), 418-448. MR 1143231 (93c:46106)
  • [2] C. M. Edwards and G. T. Rüttimann, On the facial structure of the unit balls in a $ JB{W^{\ast}}$-triple and its dual, J. London Math. Soc. (2) 38 (1988), 317-332. MR 966303 (90b:46129)
  • [3] S. Heinrich, The differentiability of the norm in spaces of operators, Funct. Anal. Appl. 9 (1975), 360-362. MR 0390834 (52:11657)
  • [4] R. V. Kadison and J. R. Ringrose, Fundamentals of the theory of operator algebras. I, II, Academic Press, New York and London, 1983, 1986.
  • [5] F. Kittaneh and R. Younis, Smooth points of certain operator spaces, Integral Equations Operator Theory 13 (1990), 849-855. MR 1073855 (91h:47041)
  • [6] R. R. Phelps, Convex functions, monotone operators and differentiability, Lecture Notes in Math., vol. 1364, Springer, Berlin, Heidelberg, and New York, 1989. MR 984602 (90g:46063)
  • [7] M. Takesaki, Theory of operator algebras. I, Springer, Berlin, Heidelberg, and New York, 1979. MR 548728 (81e:46038)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46L10, 46B07

Retrieve articles in all journals with MSC: 46L10, 46B07


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1149980-6
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society