On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces

Abstract

We prove that any non-archimedean metrizable locally convex space E with a regular orthogonal basis has the quasi-equivalence property, i.e. any two orthogonal bases in E are quasi-equivalent. In particular, the power series spaces, the most known and important examples of non-archimedean nuclear Frechet spaces, have the quasi-equivalence property. We also show that the Frechet spaces: K^N, c_0xK^N, c_0^N have the quasi-equivalence property.