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  • Proceedings of the Edinburgh Mathematical Society, Volume 40, Issue 2
  • June 1997, pp. 375-381

A remark on the tensor product of two maximal operator spaces

  • Christian Le Merdy (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091500023816
  • Published online: 01 June 1997
Abstract

Given a Banach space E, let us denote by Max(E) the largest operator space structure on E. Recently Paulsen-Pisier and, independently, Junge proved that for any Banach spaces E, F, isomorphically where and respectively denote the Haagerup tensor product and the spatial tensor product of operator spaces. In this paper we show that, in general, this equality does not hold completely isomorphically.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.D. Blecher , Tensor products of operator spaces II, Canad. J. Math. 44 (1992), 7590.

2.D. Blecher , The standard dual of an operator space, Pacific J. Math. 153 (1992), 1530.

3.D. Blecher and V. Paulsen , Tensor products of operator spaces, J. Funct. Anal. 99 (1991), 262292.

5.M. Junge and G. Pisier , Bilinear forms on exact operator spaces and B(H)⊗B(H), Geom. Funct. Anal. 5 (1995), 329363.

6.E. Effros and Z.-J. Ruan , A new approach to operator spaces, Canad. Math. Bull. 34 (1991), 329337.

7.E. Effros and Z.-J. Ruan , Self duality for the Haagerup tensor product and Hilbert space factorization, J. Funct. Anal. 100 (1991), 257284.

8.V. Paulsen , Representations of function algebras, abstract operators spaces and Banach space geometry, J. Funct. Anal. 109 (1992), 113129.

10.G. Pisier , Factorization of linear operators and geometry of Banach spaces (CBMS Regional Conference Series 60, 1986).

11.G. Pisier , Similarity problems and completely bounded maps (Lecture Notes 1618, Springer Verlag, 1996).

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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