SCHAUDER BASIS AND SEQUENCER SPACES IN GENERAL TOPOLOGICAL VECTOR SPACES

C. G.   Moorthy; I. R. Saminathan

SCHAUDER BASIS AND SEQUENCER SPACES IN GENERAL TOPOLOGICAL VECTOR SPACES

Authors

C. G. Moorthy Department of Mathematics, Alagappa University, Karaikudi-630004, Tamil Nadu, India
I. R. Saminathan Department of Mathematics, Loyola College (Autonomous), Chennai-600034, Tamil Nadu, India

Keywords:

Directed set, Net, Schauder basis, Topological vector space

Abstract

Minkowski functionals of balanced neighbourhoods of zero are used to define sequence spaces in which sequences are sequences in general non locally convex topological vector spaces. The classical result “Every basis in a complete metrizable \linebreak topological vector space is a Schauder basis” is generalized for such sequence spaces.