Интерполяционные свойства положительных операторов, ограниченных на конусах в банаховых пространствах числовых последовательностей, и их применение к теории базисов в пространствах Фреше

Abstract

An approach is presented for solving the problem of the existence of a basis in an arbitrary complemented subspace of the nuclear Köthe space with a regular basis. This approach is based on the use of interpolation properties of positive operators acting in sequence spaces and bounded on some cones embedded in them.