Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONDITIONAL EXPECTATIONS GENERATING THE COMMUTANTS OF SUBALGEBRAS OF $L^{\infty}$

  • Lambert, Alan (Department of Mathematics University of North Carolina at Charlotte)
  • Published : 1999.07.01
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Abstract

Given a probability space and a subsigma algebra A, each measure equivalent to the probability measure generates a different conditional expectation operator. We characterize those which act boundedly on the original $L^2$ space, and show there are sufficiently many such conditional expectations to generate the commutant of $L^{\infty}$ (A).

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References

  1. Pacific J. Math. v.15 Contractive projections on an L₁-space R.G. Douglas
  2. Proceedings of the Royal Soc. fo Edinburgh v.118A localising sets for sigma-algebras and related point transformations A.Lambert
  3. Proceedings of the American Math. Soc. v.123 no.3 Descriptions of conditional expectations induced by non-measure preserving transformations A.Lambert;B.M. Weinstock
  4. A Hilbert $T^*$-module view of some spaces of operators related to probabilistic conditional expectation, tp appear in Quaestiones Mathematicae A. Lambert