Some New Results on Frechet Spaces with Nuclear Kothe Quotients

Construction and Existence of separable Frechet spaces with nuclear Kothe quotients

Abstract

Our aim is to construct a separable Frechet non-Banach Space X with a continuous norm to have a quotient Y with a continuous norm and a basis .Here in addition, Y can be chosen to be nuclear, we say that X has a nuclear Kothe quotients. It can also be shown that there always exists a Frechet space which has a nuclear Kothe subspace iff it has non-Banach subspace which admits continuous norm.