A Non Standard Approach of Some Vector Lattice Concepts

Rodica-Mihaela D¿ne¿

ISBN 10: 3659534994 / ISBN 13: 9783659534997

Editore: LAP LAMBERT Academic Publishing Apr 2014, 2014

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Neuware -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 useful to academics but also to any individual who is interested in research and development of the theory of these spaces.Books on Demand GmbH, Überseering 33, 22297 Hamburg 88 pp. Englisch. Codice articolo 9783659534997

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Titolo: A Non Standard Approach of Some Vector ...

Casa editrice: LAP LAMBERT Academic Publishing Apr 2014

Data di pubblicazione: 2014

Legatura: Taschenbuch

Condizione: Neu

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Riassunto:

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 useful to academics but also to any individual who is interested in research and development of the theory of these spaces.

L'autore:

Rodica-Mihaela Dăneț Is a PhD Prof. at the Technical University of Civil Engineering Bucharest and works in the areas of Ordered Vector Spaces Theory and Fixed Point Theory for Multimaps. She leads a working group aimed to change the teaching of math in technical universities by including in lectures an informal part and engineering applications.