We show three Hahn-Banach type extension criteria for (sets of) bounded C*-linear maps of Hilbert C*-modules to the underlying C*-algebras of coefficients. One criterion establishes an alternative description of the property of C*-algebras to be monotone complete or additively complete.

In this paper, we will define a signed Lattice measure on σ-algebras, as well as give the definition of positive and negative Lattice. Herein, we will show that the Hahn Decomposition Theorem decomposes any space X into a positive lattice A and a negative Lattice B such that A∨B =X and the signed Lattice measure of A ∧ B is 0.

These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

In this paper, we introduce a weak form of amenability on topological semigroups that call $$\varphi $$ -amenability, where is character semigroup. Some basic properties new notion are obtained and by giving some examples, show definition weaker than the semigroups. As noticeable result, for semigroup S, it shown if S -amenable, then amenable. Moreover, -ergodicity introduced proved under condi...

We show that if X is a separable Banach space (or more generally a Banach with an infinite-dimensional separable quotient) then there is a continuous mapping f : X → X such that the autonomous differential equation x′ = f(x) has no solution at any point. In order to put our results into context, let us start by formulating the classical theorem of Peano. Theorem 1. (Peano) Let X = R, f : R×X → ...