On the selection of basic orthogonal sequences in non-archimedean metrizable locally convex spaces

Abstract

Our main result follows that any infinite-dimensional sub-space F of a non-archimedean metrizable locally convex space E with an or- thogonal basis (e_n) contains a basic orthogonal sequence equivalent to a block basic orthogonal sequence relative to (e_n). Hence any infinite-dimensional non-archimedean metrizable locally convex space F has a basic orthogonal sequence equivalent to a block basic orthogonal sequence relative to an orthogonal basis in c_0^N.