Functional Analysis

Math 565, Winter 2026

Class info Lecture: TueThu 10:05–11:25 Classroom: BURN 920 Course outline Zoom link (email instructor for the passcode)

Instructor Anush Tserunyan Office: BURN 915 Office hours: TueThu 16:05–17:00

Lectures Lecture 2 – 2026.01.08 Lecture 1 – 2026.01.06

Homework Homework 1 (partial)

Spectral measure

Textbooks and other resources

• J. CONWAY, A Course in Functional Analysis, 2nd ed.
• G. FOLLAND, Real Analysis: Modern Techniques and Their Applications, 2nd ed. (Chapters 5–7)
• T. TAO’s blog: course 245A and 245B
• A. TSERUNYAN, Real Analysis and Measure Theory (Math 564, Fall 2025) [webpage]

Assessment

• Maximum of (25% homework + 25% midterm + 50% final) and (25% homework + 75% final).
• There will be 6 homework assignments (one every two weeks) submitted on Crowdmark.
• The midterm will be held on February 17 in class. The date of the final will be determined later by the exam office.

Topics

1. Banach spaces
1. Examples (including spaces of measures),
2. Criterion of completeness for normed vector spaces
3. L^p spaces