Some Applications Of Functional Analysis

Abstract

Abstract

In this thesis we study the concept of

completespaces , We process this concept on

some spaces (Normed spaces –Banach spaces –

Hilbert spaces),discuss some fundamental

theorem's by using the concept of completeness

to support the concept of extension for linear

functions (Hahn – Banach theorem's ) together

with linear operators (uniform boundedness

principle ) .we study open and closed

linearsoperators as an Introduction to The closed

graph theorem .We apply thesetheorems to solve

and prove some problems and theorems,

andfinally we consider calculus on Normed spaces.