Abstract
One indicates how to construct the reduction of an arbitrary positive projection in
to a strictly positive one and one proves that the latter is “almost” the operator of the conditional mathematical expectation relative to some σ-sub-algebra. More exactly, one shows a method of selecting from a strictly positive projection an operator of “conditional mathematical expectation type” (this concept is introduced in the paper).
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Literature cited
R. G. Douglas, “Contractive projections on an L1 space,” Pac. J. Math.,15, 443–462 (1965).
D. E. Wulbert, “A note on the characterization of conditional expectation operators,” Pac. J. Math.,34, 285–288 (1970).
B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces, Wolters-Noordhoff, Groningen (1967).
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 47, pp. 172–174, 1974.
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Kulakova, V.G. Positive projections and conditional mathematical expectations. J Math Sci 9, 277–279 (1978). https://doi.org/10.1007/BF01578553
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DOI: https://doi.org/10.1007/BF01578553