Almost $\sigma $-Dedekind complete Riesz spaces and the main inclusion theorem

ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES

The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...

Riesz Type Theorem in Locally Convex Spaces

The present paper is concerned with some representatons of linear mappings of continuous functions into locally convex vector spaces, namely Theorem. If X is a complete Hausdorff locally convex vector space, then a general form of weakly compact mapping T : C[a, b] → X is of the form Tg = ∫ b a g(t)dx(t), where the function x(·) : [a, b] → X has a weakly compact semivariation on [a, b]. This th...

The Riesz representation theorem

A Riesz decomposition theorem on harmonic spaces without positive potentials

In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic...

The Operator Fejér-Riesz Theorem

The Fejér-Riesz theorem has inspired numerous generalizations in one and several variables, and for matrixand operator-valued functions. This paper is a survey of some old and recent topics that center around Rosenblum’s operator generalization of the classical Fejér-Riesz theorem. Mathematics Subject Classification (2000). Primary 47A68; Secondary 60G25, 47A56, 47B35, 42A05, 32A70, 30E99.