21-640 Introduction to Functional Analysis

Units: 12.0 Department: Mathematical Sciences Related URLs: http://www.math.cmu.edu General concepts: linear spaces, bases, norms, completeness. Linear mappings: continuity, Hahn-Banach theorem and separation of convex sets, uniform boundedness, open-mapping theorem, compact operators, unbounded operators, closed operators. Duality: weak and weak* topologies, reflexivity, convexity. Adjoints: basic properties, null spaces and ranges. Sequences of bounded linear operators: weak, strong and uniform convergence. Hilbert spaces: geometry, projections, Riesz representation theorem, bilinear and quadratic forms, orthonormal sets and Fourier series. Elementary spectral theory in Banach spaces: spectra and resolvents of bounded operators, spectral theory of compact operators, Fredholm alternative.

Popularity index Rank for this semester: #769 Rank in this department: #35   Students also scheduled 98-048 Student Taught Courses (StuCo): LaT... 21-721 Probability 21-623 Complex Analysis 57-117 Choral Ensemble for Non-Majors 21-373 Algebraic Structures 21-228 Discrete Mathematics 21-356 Principles of Real Analysis II 21-241 Matrix Algebra 85-211 Cognitive Psychology 73-100 Principles of Economics

Spring 2005 times

Sec	Time	Day	Instructor	Location
A	2:30 - 3:20 pm	M	Tartar	PH 226A
		W	Tartar	PH 226A
		F	Tartar	PH 226A