Functional Analysis

Department: 
MATH
Course Number: 
7338
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every fall semester

Spectral theory of bounded and unbounded operators, major theorems of functional analysis, additional topics.

Prerequisites: 

MATH 6338

Course Text: 

At the level of Conway: A Course in Functional Analysis, 2nd edition

Topic Outline: 
  • – Review of linear operators and the Hahn–Banach Theorem.
  • Compact and self-adjoint operators on Hilbert spaces.
  • Spectral theory of compact self-adjoint operators.
  • Spectral theory of self-adjoint operators.
  • Weak and weak* topologies and Aloaglu’s Theorem.
  • Riesz Representation Theorem for C0.
  • Additional topics at instructor’s discretion as time permits. Typical additional topics may include the following (and others):
    • Topological vector spaces and the theory of distributions.
    • Banach algebras.
    • Unbounded operators.
    • Krein-Milman theorem.
    • Semigroups, Hille-Yoshida theorem.
    • Finite-dimensional Banach spaces