Some results on the Koml\`{o}s set and applications

Résumé

In this paper, we investigate more about relationships between the Koml\`{o}s (resp. pre-Koml\`{o}s) set and other known sets. Also, some new characterizations of Koml\`{o}s (resp. pre-Koml\`{o}s) property are obtained. Furthermore, we introduce and study new classes of operators that we call Koml\`{o}s (resp. pre-Koml\`{o}s) operators, we give some characterizations of these classes of operators and we study the relationships between these classes and others classes of operators.