Conjuntos equicompactos de operadores definidos en espacios de Banach

Abstract

The work deals with the study of sets of compact operators who behave in a certain sense as a single compact. Introduces the concepts of sequential equicompactness and dominated, proving the equivalence of both and which are the dual concept of collective compactness introduced by PM Anselone. It was tested in our techniques, the classic theorem compactness of T. Palmer. Discusses the relationship of this sets to the sets evenly completely continuous and obtained new characterizations of the spaces that do not contain a copy of 11. It extends the concept to the weak topology and explores relationships with the properties of Schur, of Dunford Pettis and with the sequential compactness for the weak-star topology in bidual. Finally, we get results of compactness for sets of players with certain topologies and uniform convergence theorem is generalized compactness of F. Mayoral.