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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Dimant, Verónica and Fernández-Unzueta, Maite 2015. Bilinear ideals in operator spaces. Journal of Mathematical Analysis and Applications, Vol. 429, Issue. 1, p. 57.

    Kavruk, Ali Paulsen, Vern I. Todorov, Ivan G. and Tomforde, Mark 2011. Tensor products of operator systems. Journal of Functional Analysis, Vol. 261, Issue. 2, p. 267.

    Pisier, Gilles 2003.

  • Proceedings of the Edinburgh Mathematical Society, Volume 42, Issue 2
  • June 1999, pp. 267-284

The “maximal” tensor product of operator spaces

  • Timur Oikhberg (a1) and Gilles Pisier (a2)
  • DOI:
  • Published online: 01 January 2009

In analogy with the maximal tensor product of C*-algebras, we define the “maximal” tensor product E1μE2 of two operator spaces E1 and E2 and we show that it can be identified completely isometrically with the sum of the two Haagerup tensor products: E1hE2 + E2hE1. We also study the extension to more than two factors. Let E be an n-dimensional operator space. As an application, we show that the equality E*⊗μE = E*⊗min E holds isometrically iff E = Rn or E = Cn (the row or column n-dimensional Hilbert spaces). Moreover, we show that if an operator space E is such that, for any operator space F, we have F ⊗min E = F⊗μ E isomorphically, then E is completely isomorphic to either a row or a column Hilbert space.

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