Analysis seminar

Tristan Bice, York University

“The Projection Calculus”

We derive a projection analog of the usual continuous functional calculus and show how it can be used to simplify and strengthen a number of classical results about projections in C*-algebras, particularly those of real rank zero. Specifically we outline how it can be used to

• simplify the proofs of some standard projection homotopy results, and for C*-algebras of real rank zero -
• derive strong lifting results for projections, idempotents and partial isometries,
• excise pure states exactly (i.e. without the epsilon) on projections, and
• strengthen Kadison’s transitivity theorem.