Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONDITIONAL INDEPENDENCE AND TENSOR PRODUCTS OF CERTAIN HILBERT L(sup)$\infty$-MODULES

  • Hoover, Thomas (Department of Mathematics, University of Hawaii) ;
  • Lambert, Alan (Department of Mathematics, University of North Carolina at Charlotte)
  • Published : 2001.01.01
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Abstract

Independent $\sigma$-algebras Α and Β on X, L$^2$(X, Α V Β), L$^2$(X x X, Α x Β), and the Hilbert space tensor product L$^2$(X,Α), (※Equations, See Full-text) L$^2$(X,Β), are isomorphic. In this note, we show that various Hilbert C(sup)*-algebra tensor products provide the analogous roles when independence is weakened to conditional independence.

Keywords

References

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  3. Quaestiones Mathematicae A Hilbert C*-module view of some spaces related to probabilistic conditional expectation
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