Double operator integrals: The basics

Abstract: 

In this talk I present some basic results on double operator integrals in the finite dimensional setting using matrices. We then see a result proved by Alan Mcintosh in his paper "Counterexample to a question on commutators"  where it is shown that two selfadjoint operators A,B with bounded commutator can have the property that |A|B-B|A| is unbounded.