MAT 702 Functional Analysis

Spring 2021

• Textbook: A Course in Functional Analysis (2nd Ed). Conway. Springer. ISBN 9780387972459
• Exams and homework

Spring 2017

Exams

• Exam 1
• Exam 2
• Exam 3
• Final Exam

Homework

• 1.1: Hilbert space definition and examples
• 1.2: Orthogonality in Hilbert spaces
• 1.2b: Orthogonality in Hilbert spaces, part 2
• 1.3: Linear functionals, Riesz Representation Theorem
• 1.4: Orthonormal sets and bases
• 1.5: Isomorphic Hilbert spaces; Fourier series
• 1.6: Direct sums of Hilbert spaces
• 2.1: Operators on a Hilbert space
• 2.2: Adjoint operators
• 2.3: Projections and idempotents
• 2.4a: Compact operators
• 2.4b: Compact operators; Eigenvalues
• 2.5a: Spectral theorem
• 2.5b: Spectral theorem 2
• 3.1: Banach spaces, definition and examples
• 3.2: Linear operators on normed spaces
• 3.3: Finite-dimensional normed spaces
• 3.4: Quotients and products of normed space
• 3.5: Linear functionals, dual spaces
• 3.6: Hahn-Banach theorem
• 3.7: Banach limits
• 3.10-11: Duals of quotients and subspaces, reflexivity
• 3.12a: Open Mapping Theorem
• 3.12b: Closed Graph Theorem
• 3.13: Complemented subspaces
• 3.14: Uniform Boundedness Principle
• 4.1a: Examples of TVS
• 4.1b: Locally Convex Spaces (LCS)
• 4.2: Metrizable and Normable LCS
• 4.3a: Hahn-Banach for LCS
• 4.3b: Hahn-Banach for LCS 2
• 5.1: Duality of LCS
• 5.3: Alaoglu theorem
• 5.4: Applications of weak compactness
• 5.7: Extreme points
• 5.9: Nonlinear maps and their fixed points

Spring 2014

Exams

• Exam 1
• Exam 2
• Final Exam

Spring 2012

Exams

• Exam 1
• Exam 2
• Final Exam