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  • Proceedings of the Edinburgh Mathematical Society, Volume 37, Issue 3
  • October 1994, pp. 521-537

A specific form of Grothendieck's inequality for the two-dimensional case, with applications to C*-algebras

  • G. J. O. Jameson (a1)
  • DOI: http://dx.doi.org/10.1017/S0013091500018988
  • Published online: 01 January 2009
Abstract

We characterize bilinear forms V on such that V(e, e) = ‖V‖ = 1 in terms of their matrices. For such V we prove that |V(x, y)|2≦φ(|x|2)ψ(|y|2) for all x, y, where φ(x)= V(x, e), ψ(y) = V(e, y). Some other properties of such forms are given.

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Linked references
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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.A. M. Davie , Matrix norms related to Grothendieck's inequality, in Banach Spaces (ed. N. Kalton and E. Saab , Lecture Notes in Math. 1166, Springer, Berlin1985), 2226.

2.U. Haagerup , The Grothendieck inequality for bilinear forms on C*-algebras, Adv. Math. 56 (1985), 93116.

4.G. Pisier , Grothendieck's theorem for non-commutative C*-algebras with an appendix on Grothendieck's constant. J. Funct. Anal. 29 (1978), 397415.

5.G. Pisier , Factorization of Linear Operators and Geometry of Banach Spaces (American Math. Soc., Providence1986).

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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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