Products of Conditional Expectation Operators: Convergence and Divergence

On Convergence of Conditional Expectation Operators

Given an operator T : UX(Σ) → Y or T : C(H,X) → Y , one may consider the net of conditional expectation operators (Tπ) directed by refinement of the partitions π. It has been shown previously that (Tπ) does not always converge to T . This paper gives several conditions under which this convergence does occur, including complete characterizations when X = R or when X∗ has the Radon-Nikodým prope...

Iterates of Conditional Expectation Operators

the investigation of research articles in applied linguistics: convergence and divergence in iranian elt context

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Iterates of a Product of Conditional Expectation Operators

Let (Ω,F , μ) be a probability space and let T = P1P2 · · ·Pd be a finite product of conditional expectations with respect to the sub σ-algebras F1,F2, . . . ,Fd. Since conditional expectations are contractions of all Lp(μ) spaces, p ∈ [1,∞], so is T . When d = 2, Burkholder and Chow [2] proved that for every f ∈ L2(μ) the iterates T f converge a.s. (and thus also in L2-norm) to the conditional...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...