MA 546 - Spring 2026 - Introduction to Functional Analysis

 Instructor  Plamen Stefanov
 Office  MATH 728
 Email  stefanov@math.purdue.edu
 Meeting  TueThu, 10:30 AM - 11:45 AM in SCHM 309
 Office Hours  TueThu, 1:30-2:30
 Grader  Ethan Kessinger
 Book  M.Reed and B.Simon, Functional Analysis, link

Homework

HW1, due Tue, 1/27 at midnight on Brightspace

HW2, due Tue, 2/11 at midnight on Brightspace

HW3, due Tue, 3/23 at midnight on Brightspace

Midterm Exam: Tue 03/06, 8:00-9:30pm, FRNY G124


Schedule 

Chapter I: Preliminaries
    I. Sets and functions - read it
    2. Metric and normed linear spaces
    3. Two convergence arguments - read it

Chapter II: Hilbert spaces
    1. The geometry of Hilbert space
    2. The Riesz lemma
    3. Orthonormal bases

Chapter III: Banach spaces
    1. Definition and examples
    2. Duals and double duals
    3. The Hahn-Banach theorem [Notes]
    4. Operations on Banach spaces
    5. The Baire category theorem, and its consequences

Chapter IV: Topological spaces
    1. General notions
    2. Nets and convergence
    3. Compactness (part of it)
    5. Weak topologies on Banach spaces

Chapter VI: Bounded operators
    1. Topologies in bounded operators
    2. Adjoints [Notes]