In a nutshell, functional analysis is the study of normed vector spaces and bounded linear operators. Thus it merges the subjects of linear algebra (vector spaces and linear maps) with …

After all, the development of quantum mechanics and functional analysis are intimately related. Consider then the hydrogen atom and its “spectrum”: we know it has bound states of negative …

Since most of the spaces we study are function spaces, like C(M), the functions defined on them are “functionals.” Thus “functional analysis” is the analysis of functions defined on function …

This course provides an introduction to functional analysis. This is an advanced undergraduate course for which knowledge of real analysis and linear algebra, as well as a certain degree of …

Functional analysis as we study it involves vector spaces with additional structure (a norm function). Thus linearity is always present and all the maps we consider will be linear maps.

Lp( ) is a linear space under summation and scalar multiplication. k kp is a norm (the triangle inequality is due to Minkowski's inequality). Lp is complete (Theorem 6.15 in Lecture Notes on …

Much of the material and inspiration came from Larry Brown’s lectures on functional analysis at Purdue University in the 1990s, and some came from my Reed thesis 1987.

Nahar. Preface to the Fourth Edition - December 15, 2018 Thanks to Adina Goldberg, Hayley Reid, Wanchun Shen, Erlang Surya, Wentao Yang and Zhenyuan Zhang for catching those …

Last time, we proved the Uniform Boundedness Theorem from the Baire Category Theorem, and we’ll continue to prove some “theorems with names” in functional analysis today.

These notes are intended to familiarize the student with the basic concepts, principles and methods of functional analysis and its applications, and they are intended for senior …