Transversal Functional Analysis

Milan Tasković

Mathematica Moravica, Tome 18 (2014) no. 2.

Résumé

This paper provides an introduction to the ideas and methods of transversal functional analysis based on the transversal sets theory. A unifying concept that lies at the heart of transversal functional analysis is that of a transversal normed linear space. I have developed the theory far enough to include facts of have called the three new basic principles of linear analysis as: Form of Hahn-Banach theorem, Form of Principle of Uniform Boundedness (= Form of Banach-Steinhaus theorem), and Form of Open Mapping theorem. In the classical functional analysis fundamental fact is Riesz lemma. In transversal functional analysis (on lower transversal normed spaces) its role play so-called Geometrical lemma! This paper presents applications of the Axiom of Infinite Choice.

Détail

Mots-clés : Transversal (upper, lower and middle) normed spaces, Transversal seminorms, Form of Hahn-Banach theorem, Form of Principle of Uniform Boundedness, Form of Banach-Steinhaus theorem, Form of Open Mapping theorem, Form of Riesz lemma, Geometrical lemma, Form of convergence principle, Lower compactness, Lower total continuous operators, Lower locally compactness, Lower Fredholm alternative, Extension Leray-Schauder principle, Peano’s equation, Lower compact operators