Decompositions of Weighted Conditional Expectation Type Operators

Iterates of Conditional Expectation Operators

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...

Generalized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces

Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...

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...

Essential norm estimates of generalized weighted composition operators into weighted type spaces

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...