Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Kung-Wei Yang

Second Advisor

Dr. George Whaples


I Preliminaries

The purpose of this dissertation is to extend some classical results on compact and Fredholm operators to the case in which the linear spaces involved are non-archimedean normed linear spaces over a valued field.

In Section I are listed some definitions and basic concepts that are needed for a study of non-archimedean valuation theory. The concepts of tensor products of nonarchimedean Banach spaces over a spherically complete field F, and of the tensor product of operators, are also dealt with in this section.

The proofs of most of the results in Section II are based on the known extensions of classical results such as the open mapping theorem and the Hahn-Banach theorem. These results are used repeatedly in the subsequent sections on compact and Fredholm operators.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons