Almost everywhere convergent sequences of weak∗‐to‐norm continuous operators

On the Spaces of $lambda _{r}$-almost Convergent and $lambda _{r}$-almost Bounded Sequences

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

On Lacunary Almost Convergent Sequences

The purpose of this paper is to define and study the spaces [ĉ,M, p](∆u , q, s), [ĉ,M, p, ] θ 0(∆ m u , q, s) and [ĉ,M, p, ] θ ∞(∆ m u , q, s) of lacunary convergent sequences. We also study some inclusion relations between these spaces and some properties and theorems. 2000 Mathematics Subject Classification:40D05, 40A05. 1.Introduction and definitions Let w denote the set of all complex seque...

Convergent sequences of composition operators

Composition operators Cφ on the Hilbert Hardy space H 2 over the unit disk are considered. We investigate when convergence of sequences {φn} of symbols, (i.e., of analytic selfmaps of the unit disk) towards a given symbol φ, implies the convergence of the induced composition operators, Cφn → Cφ . If the composition operators Cφn are Hilbert–Schmidt operators, we prove that convergence in the Hi...

The Three-Dimensional Gauss Algorithm Is Strongly Convergent Almost Everywhere

Incentive Compatibility: Everywhere vs. Almost Everywhere∗

A risk neutral buyer observes a private signal s ∈ [a, b], which informs her that the mean and variance of a normally distributed risky asset are s and σ s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume σ s ∈ { 0, σ } for some σ > 0 and let B = { s ∈ [a, b] | σ s = 0 } . If B = ∅, then there exists a fully revealing equilibrium in whic...