Published in Mathematica Slovaca
In this paper we investigate some fundamental properties of unital topology on a lattice ordered group with order unit. We show that some essential properties of order unit norm on a vector lattice with order unit, are valid for unital l-groups. For instance we show that for an Archimedean Riesz space G with order unit u, the unital topology and th...
Published in Lobachevskii Journal of Mathematics
We consider linear normed spaces of measurable functions dominated by positive measurable function powered by real positive parameter. Also, we consider its dual and predual, and we propose a method for constructing a limit spaces of these functional spaces taken by power parameter. We prove that these limit spaces are (LF)-spaces and also prove th...
Published in Milan Journal of Mathematics
In a recent paper, F. Boca investigates the AF algebra \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathfrak{A}}}$$\end{document} associated with the Farey-Stern-...
Published in Algebra universalis
We give a new proof for McNaughton’s Theorem on finitely generated free MV-algebras, using a free abelian ℓ-group on a po-group.
Published in Positivity
We prove that an order unit can be adjoined to every L∞-matricially Riesz normed space. We introduce a notion of strong subspaces. The matrix order unit space obtained by adjoining an order unit to an L∞-matrically Riesz normed space is unique in the sense that the former is a strong L∞-matricially Riesz normed ideal of the later with codimension o...
