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)

 
 

 

The norm of a derivation in a $ W\sp{\ast} $-algebra


Author: László Zsidó
Journal: Proc. Amer. Math. Soc. 38 (1973), 147-150
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1973-0326412-6
MathSciNet review: 0326412
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The norm of an inner derivation $ {\delta _a}$ of a (nonnecessary separable) $ {W^ \ast }$-algebra $ M$ is shown to satisfy

$\displaystyle \vert\vert{\delta _a}\vert\vert = 2\inf \{ \vert\vert a - z\vert\vert;z \in Z,\;{\text{the center of}\; M\} ,}$

and some related results are obtained.

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

  • [1] J. Dixmier, Les algèbres d'opérateurs dans l'espace hilbertien (Algèbres de von Neumann), 2ième éd., Gauthier-Villars, Paris, 1969.
  • [2] -, Sur certains espaces considérés par M. H. Stone, Summa Brasil Math. 2 (1951), 151-182. MR 14, 69. MR 0048787 (14:69e)
  • [3] P. Gajendragadkar, Thesis, Indiana University, Bloomington, Ind., 1970.
  • [4] J. G. Glimm, A Stone-Weierstrass theorem for $ {C^ \ast }$-algebras, Ann. of Math. (2) 72 (1960), 216-244. MR 22 #7005. MR 0116210 (22:7005)
  • [5] H. Halpern, Irreducible module homomorphisms of a von Neumann algebra into its center, Trans. Amer. Math. Soc. 140 (1969), 195-221. MR 39 #3322. MR 0241987 (39:3322)
  • [6] R. V. Kadison, E. C. Lance and J. R. Ringrose, Derivations and automorphisms of operator algebras. II, J. Functional Analysis 1 (1967), 204-221. MR 35 #5954. MR 0215111 (35:5954)
  • [7] S. Sakai, Derivations of $ {W^ \ast }$-algebras, Ann. of Math. (2) 83 (1966), 273-279. MR 33 #1748. MR 0193528 (33:1748)
  • [8] J. G. Stampfli, The norm of a derivation, Pacific J. Math. 33 (1970), 737-747. MR 42 #861. MR 0265952 (42:861)

Similar Articles

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

Retrieve articles in all journals with MSC: 46L10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0326412-6
Keywords: $ {W^ \ast }$-algebra, hyperstonean space, derivation
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society