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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Popescu, Gelu 2006. Commutator lifting inequalities and interpolation. Pacific Journal of Mathematics, Vol. 225, Issue. 1, p. 155.

    Popescu, Gelu 2004. Multivariable moment problems. Positivity, Vol. 8, Issue. 4, p. 339.

    Popescu, Gelu 2003. Multivariable Nehari problem and interpolation. Journal of Functional Analysis, Vol. 200, Issue. 2, p. 536.

    Popescu, Gelu 2003. Similarity and ergodic theory of positive linear maps. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2003, Issue. 561,

    Popescu, Gelu 2002. Meromorphic interpolation in several variables. Linear Algebra and its Applications, Vol. 357, Issue. 1-3, p. 173.

    Popescu, Gelu 2002. Central Intertwining Lifting, Suboptimization, and Interpolation in Several Variables. Journal of Functional Analysis, Vol. 189, Issue. 1, p. 132.

  • Proceedings of the Edinburgh Mathematical Society, Volume 44, Issue 2
  • June 2001, pp. 389-406


  • Gelu Popescu (a1)
  • DOI:
  • Published online: 20 January 2009

A non-commutative multivariable analogue of Parrott’s generalization of the Sz.-Nagy–Foia\c{s} commutant lifting theorem is obtained. This yields Tomita-type commutant results and interpolation theorems (e.g. Sarason, Nevanlinna–Pick, Carathéodory) for $F_n^\infty\,\bar{\otimes}\,\M$, the weakly-closed algebra generated by the spatial tensor product of the non-commutative analytic Toeplitz algebra $F_n^\infty$ and an arbitrary von Neumann algebra $\M$. In particular, we obtain interpolation theorems for bounded analytic functions from the open unit ball of $\mathbb{C}^n$ into a von Neumann algebra.

A variant of the non-commutative Poisson transform is used to extend the von Neumann inequality to tensor algebras, and to provide a generalization of the functional calculus for contractive sequences of operators on Hilbert spaces. Commutative versions of these results are also considered.

AMS 2000 Mathematics subject classification: Primary 47L25; 47A57; 47A60. Secondary 30E05

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
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