University of Connecticut

Course Info

MATH 5130: Functional Analysis I

Description: Theory of Banach spaces: duality, reflexivity, weak and weak* topologies. Hahn-Banach, Banach-Steinhaus, Banach-Alaoglu theorems. Krein-Milman theorem. Linear operators: compact, integral, trace class, Fredholm, Hilbert-Schmidt, Toepliz, Volterra. Commutative Banach and C*-algebras, Gelfand transform and the spectral theorem for bounded normal operators. Compact self-adjoint operators with applications to the classical Sturm-Liouville theory. Other topics in functional analysis at the choice of the instructor (e.g. unbounded self-adjoint operators, distributions, Banach algebra L1, Kaplansky density theorem, Gelfand-Naimark-Segal construction, introduction to von Neumann algebras and non-commutative integration, introduction to unbounded self-adjoint operators and the role of the Fourier transform).

Prerequisites: MATH 5111.

Credits: 3

Sections: Fall 2009 on Storrs Campus

Course Sec Comp Time Room Instructor
5130 001 Lecture TuTh 2:00-3:15 MSB315 Bass, Richard