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The maximal operator space of a normed space

Published online by Cambridge University Press:  20 January 2009

Vern I. Paulsen
Vern I. Paulsen
Affiliation:
Department of MathematicsUniverity of HoustonTexas 77204–3476, U.S.A.
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Abstract

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We obtain some new results about the maximal operator space structure which can be put on a normed space. These results are used to prove some dilation results for contractive linear maps from a normed space into B(H). Finally, we prove CB(MIN(X), MAX(y)) = Γ2(X, Y) and apply this result to prove some new Grothendieck-type inequalities and some new estimates on spans of “free” unitaries.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 2 , June 1996 , pp. 309 - 323
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Blecher, D. B., Tensor products of operator spaces II, Canad. J. Math. 44 (1992), 75–90.CrossRefGoogle Scholar
2. Blecher, D. B., The standard dual of an operator space, Pacific J. Math. 153 (1992), 15–30.CrossRefGoogle Scholar
3. Blecher, D. B. and Paulsen, V. I., Tensor products of operator spaces, J. Fund. Anal. 99 (1991), 262–292.CrossRefGoogle Scholar
4. Christensen, E., Effros, E. and Sinclair, A., Completely bounded maps and C* algebraic cohomology, Invent. Math. 90 (1987), 279–296.CrossRefGoogle Scholar
5. Effros, E. and Ruan, Z. J., Self duality for the Haagerup tensor product and Hilbert space factorization, J. Fund. Anal. 100 (1991), 257–284.CrossRefGoogle Scholar
6. Effros, E. and Ruan, Z. J., The Grothendieck-Pietsch and Dvoretsky-Rogers theorems for operator spaces, J. Fund. Anal., to appear.Google Scholar
7. Junge, M. and Pisier, G., Bilinear forms on exact operator spaces and B(H) ⊗ B(H), GAFA 5 (1995), 329–363.Google Scholar
8. Mathes, D. B. and Paulsen, V. I., Operator ideals and operator spaces, Proc. Amer. Math. Soc. 123 (1995), 1763–1772.CrossRefGoogle Scholar
9. Paulsen, V. I. Completely bounded maps and dilations (Pitman Research Notes, 146, Longman, 1986).Google Scholar
10. Paulsen, V. I., Representations of function algebras, abstract spaces and Banach space geometry, J. Fund. Anal. 109 (1992), 113–129.CrossRefGoogle Scholar
11. Pisier, G., Factorization of linear operators and the geometry of Banach spaces (CBMS Regional Conference Series 60, 1986), reprinted 1987.CrossRefGoogle Scholar
12. Ruan, Z. J., Subspaces of C*-algebras, J. Fund. Anal. 76 (1988), 217–230.CrossRefGoogle Scholar
13. Zhang, C., Representation and Geometry of Operator Spaces (Thesis, University of Houston, 1994).Google Scholar
14. Zhang, C., Representations of operator spaces, J. Operator Th. 33 (1995), 327–351.Google Scholar