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.
@article{1267798505,
author = {Piszczek, Krzysztof},
title = {On a property of PLS-spaces inherited by their tensor products},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {17},
number = {1},
year = {2010},
pages = { 155-170},
language = {en},
url = {http://dml.mathdoc.fr/item/1267798505}
}
Piszczek, Krzysztof. On a property of PLS-spaces inherited by their tensor products. Bull. Belg. Math. Soc. Simon Stevin, Tome 17 (2010) no. 1, pp. 155-170. http://gdmltest.u-ga.fr/item/1267798505/