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Operator Algebra and Noncommutative Geometry Seminar Series
July 11, 2019 @ 3:30 pm - 4:30 pm
Asst Prof Chris Bourne (Tohoku University) will be giving a talk.
The Cayley transform and K-theory
The Cayley transform is a way to pass between unitary operators and self-adjoint (generally unbounded) operators on a Hilbert space or C*-module. I will review this construction and its application to an isomorphism between K-theory and Kasparov modules. Time permitting, I will also introduce a Z_2-graded analogue of this transform and its application to van Daele K-theory for graded C*-algebras. Explicit isomorphisms for all 8 real K-theory groups are a special case of this map. This is joint work with Johannes Kellendonk and Adam Rennie.