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3 results

  • ORDER EMBEDDING OF A MATRIX ORDERED SPACE

  • Part of
  • ANIL K. KARN
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 84 / Issue 1 / August 2011
    Published online by Cambridge University Press:
    21 June 2011, pp. 10-18
    Print publication:
    August 2011
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  • We characterize certain properties in a matrix ordered space in order to embed it in a C*-algebra. Let such spaces be called C*-ordered operator spaces. We show that for every self-adjoint operator space there exists a matrix order (on it) to make it a C*-ordered operator space. However, the operator space dual of a (nontrivial) C*-ordered operator space cannot be embedded in any C*-algebra.

  • THE OPERATOR SHIFT SPACE

  • Timur Oikhberg
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 1 / February 2008
    Published online by Cambridge University Press:
    04 February 2008, pp. 229-263
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  • We construct and examine an operator space $X$, isometric to $\ell_2$, such that every completely bounded map from its subspace $Y$ into $X$ is a compact perturbation of a linear combination of multiples of a shift of given multiplicity and their adjoints. Moreover, every completely bounded map on $X$ is a Hilbert–Schmidt perturbation of such a linear combination.