## Lethbridge Analysis Seminar: Berndt Brenken

- Date: 10/28/2016
- Time: 12:00

*University of Calgary*

University of British Columbia

Partial Isometries and Operator Algebras of ordered *-semigroups.

A C-algebra is a norm closed algebra of bounded operators on a Hilbert space which is closed under taking adjoints. Types of operators such as unitaries, projections, and partial isometries are described. A uni-

tary operator implements a -automorphism, and representing groups via unitary operators on Hilbert space lead to considering operator algebras incorporating dynamics from group actions.

Similarly one can consider the map implemented by a partial isometry. Although not a homomorphism it is a linear map with order preserving properties. We consider semigroups, a class containing groups and inverse semigroups, and introduce order structures involving matrices.

The algebra generated by a partial isometry can be described as the algebra arising from a complete positive map acting on a -semigroup.

Location: Room D634