Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T16:25:06.384Z Has data issue: false hasContentIssue false
  • English
  • Français

On the convergence of a sequence of completely positive maps to the identity

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

George A. Elliott
George A. Elliott
Affiliation:
Department of Mathematics University of TorontoTorontoCanadaM5S 3G3 Department of Mathematics University of CopenhagenCopenhagenDenmark The Fields Institute222 College Street TorontoCanadaM5T 3J1 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that a sequence of completely positive linear maps on a W*-algebra that converges pointwise in norm to the identity converges uniformly.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 340 - 348
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Akemann, C. A., ‘Sequential convergence in the dual of a W*-algebra’, Comm. Math. Phys. 7 (1968), 222–224.CrossRefGoogle Scholar
[2]Choi, M.-D., ‘A Schwarz inequality for positive linear maps on C*-algebras’, Illinois J. Math. 18 (1974), 565–574.CrossRefGoogle Scholar
[3]Coulhon, T., ‘Suites d'opérateurs sur un espace C(K) de Grothendieck’, C. R. Acad. Sci. Paris Sér. I Math. 298 (1984), 13–15.Google Scholar
[4]Coulhon, T. and Raynaud, Y., ‘Convergence vers l'identité de suites d'opérateurs définis sur L(H)’, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), 111–113.Google Scholar
[5]Elliott, G. A., ‘Convergence of automorphisms in certain C*-algebras’, J. Funct. Anal. 16 (1972), 204–206.CrossRefGoogle Scholar
[6]Elliott, G. A., ‘On derivations of AW*-algebras’, Tôhoku Math. J. 30 (1978), 263–276.CrossRefGoogle Scholar
[7]Groh, U., ‘Norm continuity of strongly continuous semigroups on W*-algebras’, in: Semesterbericht Funktionalanalysis Tübingen, Wintersemester 1983–1984.Google Scholar
[8]Kallman, R. R., ‘Uniform continuity, unitary groups, and compact operators’, J. Funct. Anal. 1 (1967), 245–253.CrossRefGoogle Scholar
[9]Kallman, R. R., ‘Unitary groups and automorphisms of operator algebras’, Amer. J. Math. 91 (1969), 785–806.CrossRefGoogle Scholar
[10]Kallman, R. R., ‘One-parameter groups of *-automorphisms of II1 von Neumann algebras’, Proc. Amer. Math. Soc. 24 (1970), 336–340.Google Scholar
[11]Kishimoto, A. and Robinson, D. W., ‘Subordinate semigroups and order properties’, J. Austral. Math. Soc. Ser. A 31 (1981), 59–76.CrossRefGoogle Scholar
[12]Lotz, W. P., ‘Uniform convergence of operators on L∞ and similar spaces’, Math. Zeit. 190 (1985), 207–220.CrossRefGoogle Scholar