Introduction to Functional Analysis

Calendar

LEC #	TOPICS	KEY DATES
1	Basic Banach Space Theory
2	Bounded Linear Operators	Assignment 1 due
3	Quotient Spaces, the Baire Category Theorem and the Uniform Boundedness Theorem
4	The Open Mapping Theorem and the Closed Graph Theorem	Assignment 2 due
5	Zorn’s Lemma and the Hahn-Banach Theorem
6	The Double Dual and the Outer Measure of a Subset of Real Numbers	Assignment 3 due
7	Sigma Algebras
8	Lebesgue Measurable Subsets and Measure	Assignment 4 due
9	Lebesgue Measurable Functions
10	Simple Functions	Assignment 5 due
11	The Lebesgue Integral of a Nonnegative Function and Convergence Theorems
	Midterm Exam	Midterm Exam due
12	Lebesgue Integrable Functions, the Lebesgue Integral and the Dominated Convergence Theorem
13	Lp Space Theory
14	Basic Hilbert Space Theory	Assignment 6 due
15	Orthonormal Bases and Fourier Series
16	Fejer’s Theorem and Convergence of Fourier Series	Assignment 7 due
17	Minimizers, Orthogonal Complements and the Riesz Representation Theorem
18	The Adjoint of a Bounded Linear Operator on a Hilbert Space	Assignment 8 due
19	Compact Subsets of a Hilbert Space and Finite-Rank Operators
20	Compact Operators and the Spectrum of a Bounded Linear Operator on a Hilbert Space	Assignment 9 due
21	The Spectrum of Self-Adjoint Operators and the Eigenspaces of Compact Self-Adjoint Operators
22	The Spectral Theorem for a Compact Self-Adjoint Operator	Assignment 10 due
23	The Dirichlet Problem on an Interval
	Final Assignment	Final Assignment due