*Correspondence: [email protected] School of Mathematical Sciences, Dalian University of Technology, Dalian, P.R. China Abstract In this paper, we improve the concept of Cm-almost periodicity on periodic time scales. The concept is based on the revised definition of almost periodicity introduced by Wang and Agarwal in 2015. A theorem is derived for the relationship of Cm-almost periodic func...

The von Neumann algebra free product of arbitary finite dimensional von Neumann algebras with respect to arbitrary faithful states, at least one of which is not a trace, is found to be a type III factor possibly direct sum a finite dimensional algebra. The free product state on the type III factor is what we call an extremal almost periodic state, and has centralizer isomorphic to L(F∞). This a...

where a and W satisfy (a1) a(t) is a continuous almost periodic function of t with a(t) ≥ a0 > 0 for all t ∈ R. (W1) There is a ξ ∈ R\{0} such that W ∈ C(R\{ξ},R). (W2) limx→ξW (x) = −∞. (W3) There is a neighborhood N of ξ and U ∈ C(N\{ξ},R) such that |U(x)| → ∞ as x→ ξ and |U ′(x)|2 ≤ −W (x) for x ∈ N\{ξ}, (W4) W (x) < W (0) = 0 if x 6= 0 and W ′′(0) is negative definite. (W5) There is a const...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

An almost Moore digraph G of degree d > 1, diameter k > 1 is a diregular digraph with the number of vertices is one less than the Moore bound. If G is an almost Moore digraph, then for each vertex u ∈ V (G) there exists a vertex v ∈ V (G), called repeat of u and denoted by r(u) = v, Such that there are two walks of lenght ≤ k from u to v. The smallest positive integer p such that the compositio...

In this paper we give some sufficient conditions, which ensure the existence of pseudo almost periodic solutions to some classes of non-autonomous first-order partial neutral functional-differential with unbounded delay. c © 2006 Elsevier Ltd. All rights reserved.

Let G be a locally compact group, and let WAP(G) denote the space of weakly almost periodic functions on G. We show that, if G is a [SIN]-group, but not compact, then the dual Banach algebra WAP(G)∗ does not have a normal, virtual diagonal. Consequently, whenever G is an amenable, non-compact [SIN]-group, WAP(G)∗ is an example of a Connes-amenable, dual Banach algebra without a normal, virtual ...

Let {T (t)} t≥0 be a C-semigroup on a Banach space X with generator A. We will investigate the asymptotic almost periodicity of {T (t)} via the Hille-Yosida space of its generator.