FUNCTIONAL ANALYSIS 1

Instructor: Paul Robinson (414 Little Hall; paulr@ufl.edu)

Class: MWF 7; LIT 223

Office: M 8; W 6; F 4

This course will focus primarily upon bounded linear operators on Hilbert space. After some preliminaries on Hilbert spaces themselves, we shall consider bounded linear operators in some detail: adjunction ("conjugate transpose") gives rise to several classes of operators (including normal, selfadjoint, unitary, isometry, coisometry); we shall investigate these and others, both abstractly and in concrete Hilbert spaces. Among the topics included will be the spectrum and the numerical range, both of which generalize the notion of eigenvalue. 

Grades will be assigned on the basis of performance in regular homework assignments. 

Text: None is required (but see references below). 

Homeworks

References 

Class lecture notes should be sufficient, but the following texts may be consulted with  (considerable) profit.

Conway: A Course in Functional Analysis (Springer GTM) 

Kadison & Ringrose: Fundamentals of the Theory of Operator Algebras Volume 1 (Academic Press) 

Pedersen: Analysis NOW (Springer GTM)

Rudin: Functional Analysis (McGraw-Hill)