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The minimal operator module of a Banach module

Published online by Cambridge University Press:  20 January 2009

Bojan Magajna
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19 Ljubljana 1000, Slovenia, E-mail address: [email protected]
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Banach modules over C*-algebras (von Neumann algebras) that can be represented isometrically as operator modules (normal operator modules, respectively) are characterised.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Arveson, W. B., Subalgebras of C*-algebras, Acta Math. 123 (1969), 141224.CrossRefGoogle Scholar
2.Blecher, D. P., The standard dual of an operator space, Pacific J. Math. 153 (1992), 1530.CrossRefGoogle Scholar
3.Blecher, D. P., A completely bounded characterisation of operator algebras, Math. Ann. 303 (1995), 227239.CrossRefGoogle Scholar
4.Blecher, D. P. and Paulsen, V. I., Tensor products of operator spaces, J Funct. Anal. 99 (1991), 262292.CrossRefGoogle Scholar
5.Blecher, D. P., Ruan, Z.-J. and Sinclair, A. M., A characterisation of operator algebras, J. Funct. Anal. 89 (1990), 188201.CrossRefGoogle Scholar
6.Christensen, E., Effros, E. G. and Sinclair, A., Completely bounded multilinear maps and C*-algebraic cohomology, Invent. Math. 90 (1987), 279296.CrossRefGoogle Scholar
7.Effros, E. G. and Kishimoto, A., Module maps and Hochschild-Johnson cohomology, Indiana Univ. Math. J. 36 (1987), 257276.CrossRefGoogle Scholar
8.Effros, E. G. and Ruan, Z.-J., Representation of operator bimodules and their applications, J. Operator Theory 19 (1988), 137157.Google Scholar
9.Effros, E. G. and Ruan, Z.-J., On the abstract characterisation of operator spaces, Proc. Amer. Math. Soc. 119(1993), 579584.CrossRefGoogle Scholar
10.Kadison, R. V. and Ringrose, J. R., Fundamentals of the theory of operator algebras. Vols. 1, 2 (Academic Press, London, 1983, 1986).Google Scholar
11.Magajna, B., Strong operator modules and the Haagerup tensor product, Proc. London Math. Soc. 74 (1997), 201240.CrossRefGoogle Scholar
12.Magajna, B., A topology for operator modules over W*-algebras, J Funct. Anal. 154 (1998), 1741.CrossRefGoogle Scholar
13.Paulsen, V. I., Completely bounded maps and dilations (Research Notes in Math., Vol. 146, Pitman, London, 1986).Google Scholar
14.Paulsen, V. I., The maximal operator space of a normed space, Proc. Edinburgh Math. Soc. 39 (1996), 309323.CrossRefGoogle Scholar
15.Pedersen, G. K., Analysis now (Graduate Texts in Math. 118, Springer-Verlag, Berlin, 1989).CrossRefGoogle Scholar
16.Pisier, G., Similarity problems and completely bounded maps (Lecture Notes in Math. 1618, Springer-Verlag, Berlin, 1996).CrossRefGoogle Scholar
17.Ruan, Z. J., Subspaces of C* -algebras, J. Funct. Anal. 76 (1988), 217230.CrossRefGoogle Scholar
18.Sinclair, A. M. and Smith, R. R., Hochschild cohomology of von Neumann algebras (London Math. Soc. Lecture Note Series, Vol. 203, Cambridge Univ. Press, Cambridge, 1995).CrossRefGoogle Scholar
19.Takesaki, M., Theory of operator algebras I (Springer-Verlag, New York, 1979).CrossRefGoogle Scholar
20.Varoupoulos, N. T., A theorem on operator algebras, Math. Scand. 37 (1975), 173182.CrossRefGoogle Scholar