Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-15T09:30:24.217Z Has data issue: false hasContentIssue false
  • English
  • Français

Extension of completely bounded A-B bimodule maps†

Published online by Cambridge University Press:  18 May 2009

Paul S. Muhly  and
Qiyuan Na
Paul S. Muhly
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A.
Qiyuan Na
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242, U.S.A.
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.

In this paper, we present an “order” characterization of completely bounded bimodule maps for bimodules over unital operator algebras. We use this result to prove a bimodule generalization of Wittstock's generalized Hahn-Banach theorem. Our proofs simplify and unify some of Wittstock's arguments.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 2 , May 1994 , pp. 145 - 155
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

1.Blecher, D. P., Muhly, P. S., and Paulsen, V. I., Morita theory for operator algebras, Preprint.Google Scholar
2.Blecher, D. P., Ruan, Z.-J., and Sinclair, A. M., A characterization of operator algebras, J. Functional Analysis 89 (1990), 188–201.CrossRefGoogle Scholar
3.Choi, M. D. and Effros, E. G., Injectivity and operator spaces, J. Functional Analysis 24 (1977), 156–209.CrossRefGoogle Scholar
4.Edward, G. Effros and Ruan, Zhong-Jin, Representation of operator bimodules and their application, J. Operator Theory 19 (1988), 137–157.Google Scholar
5.Murphy, Gerard J., C*-algebras and operator theory(Academic Press, 1990).Google Scholar
6.Paulsen, Vern I., Completely bounded maps and dilations, Pitman Research Notes in Math. No 146 (Longmans, 1986).Google Scholar
7.Paulsen, V. I. and Smith, R. R., Multilinear maps and tensor norms on operator systems, J. Functional Analysis 73 (1987), 258–276.CrossRefGoogle Scholar
8.Ruan, Zhong-Jin, Subspaces of C*-algebras, J. Functional Analysis 76 (1988), 217–230.CrossRefGoogle Scholar
9.Smith, R. R., Completely bounded module maps and the Haagerup tensor product, J. Functional Analysis 102 (1991), 156–175.CrossRefGoogle Scholar
10.Suen, Ching-Yun, Completely bounded maps on C*-algebras, Proc. Amer. Math. Soc. 93 (1985), 81–87.Google Scholar
11.Wittstock, G., Extension of completely bounded C*-module homomorphisms, Proc. Conf. on Operator Algebras and Group Representations, Neptun, 1980 (Pitman, 1983), 238–250.Google Scholar
12.Wittstock, G., Ein operatorwertiger Hahn-Banach Satz, J. Functional Analysis 40 (1981), 127–150.CrossRefGoogle Scholar