## Quantum Topology / Hopf Algebra Seminar

Jim Otto

UIC

Operator Topologies & C* & W* Algebras

**Abstract:**We briefly review the quantum square well potential in 1 space + 1 time dimensions to see examples of Hilbert spaces, bounded linear operators, bound states, and scattering states. We review the norm and weak topologies on Hilbert spaces and the norm, strong, and weak topologies on bounded linear operators. We note the definition of, and need for, nets (rather than just sequences). We recall the definitions of rings and * algebras and of their closures to C* algebras (in the norm topology) and to W* algebras (in the weak or strong topologies). We give examples of these algebras using towers of finite dimensional algebras.

Tuesday November 28, 2017 at 3:00 PM in SEO 612