Weak*convergence of iterates of Lasota–Mackey–Tyrcha operators

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...

Iterates of Conditional Expectation Operators

Iterates of Volterra operators and indeterminate forms

During the last decades, many attempts have beenmade in order to explain and formalize mathematically a large set of phenomena that, at a first glance, are not well described by traditional theories. Among those attempts one finds the whole theory of self-organized criticality and some statistical theories. In recent years, a popular approach has been a Daróczy-like entropy [2] and its correspo...

Asymptotic behaviour of iterates of positive linear operators

We investigate the iterates of positive linear operators on C[0, 1] which preserve the linear functions, and the asymptotic behaviour of the associated semigroup. The general results are applied to the Bernstein-Schnabl operators on the unit interval.

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...