Some New Results on Normal Solvability and Schauder Theory of Compact Operators

Abstract

In this paper we shall present some results on the compact operators K   over  a  normed  linear Space E. Also the dual K will be considered. It will be shown that the dimension of the null spaces and the Co-dimensions of the image spaces of T and T are identical. If E and F are normed linear spaces and k is compact map of E into F,  then  K  is also compact .If F is a  Banach space and K is compact then the continuous map K is compact.

Keywords: Solvability, Topological Vector spaces,   Orthogonal  spaces