On a property of PLS-spaces inherited by their tensor products

Abstract

The class of PLS-spaces covers most of the natural spaces of analysis, e. g. the space of real analytic functions, spaces of distributions. We investigate the property of PLS-spaces called {\it dual interpolation estimate} and show that in many important and classical cases this property is inherited by tensor products of two PLS-spaces. We establish the inheritance if at least one of the spaces is a nuclear Fréchet space or a PLN-space. The latter includes the important, classical case when one of the spaces is the dual of a nuclear Fréchet space.