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A Non Standard Approach of Some Vector Lattice Concepts

A Non Standard Approach of Some Vector Lattice Concepts

Автор: Rodica-Mihaela Dane?

Описание:

The starting point of this work consists of several papers published by the author ten years ago. The main idea was to give algebraic descriptions and (sometimes) geometric interpretations for some basic concepts of the Vector Lattice Theory as: vector lattices, Archimedean vector lattices, sublattices, lattice-subspaces, solid subsets, ideals, (o)-dense subspaces. In addition we considered some linear operators commuting with the lattice operations such as the classical Riesz homomorphisms, but also the restricted-lattice operators and quasi-lattice operators, introduced by the author. The extension of restricted-lattice operators is studied as well. By giving algebraic descriptions of the above mentioned vector lattice concepts, the paper is a non standard approach. But, at the same time, by these algebraic descriptions of the classical definitions, the paper shows a way to generalize some notions from vector lattices to ordered vector spaces. Consequently this work is especially…

Издатель: LAP Lambert Academic Publishing

Год: 2014

Серия:

Язык: Английский

Страниц: 1

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