Some remarks about o–O pairs of Banach spaces

Abstract

In this paper we recall the definition and the properties of o–O structure given by K. M. Perfekt and show some properties that hold for this construction. The main result is that it can always be reduced to the case where the operators involved in the construction are linear functionals on the ‘‘big-O’’ space, simplifying the construction. Using this result, a series of results concerning these functionals is shown.