Operator Theory

3 credits · Graduate

This course explores the algebraic and functional analytic properties of operator algebras, focusing on C*-algebras and von Neumann algebras. Topics include: bounded operators on a Hilbert space; the spectrum of an operator; unitary and self adjoint operators; polar decomposition; Gelfand's representation theorem for commutative C*-algebras; classification of Von Neumann algebras; factors. Additional topics may include: the Gelfand-Naimark-Segal construction; the Gelfand-Naimark theorem; bimodules; Connes fusion. EXCLUSIONS: MATH 4160.03 FORMATS: Lecture