Colloquium: Triple operator integrals valued in trace class operators.
Title: Triple operator integrals valued in trace class operators.
In this talk, I will introduce few notions of noncommutative analysis. Among them, I will define important spaces such as the Hilbert-Schmidt class S^2(H) and the trace class S^1(H), where H is a Hilbert space. Those spaces can be seen as the noncommutative analogues of the usual l_2 and l_1-spaces (the spaces of square summable and summable sequences of complex numbers, respectively).
I will also define linear and bilinear Schur multipliers. Those objects are related to the Schur products of matrices and to understand them, it is enough to study them in the case of finite matrices.
Finally, I will introduce the double operator integral mappings and triple operator integral mappings associated to normal operators A,B,C on a Hilbert space H. When H is finite dimensional, those objects correspond to linear and bilinear Schur multipliers with respect to the spectral decompositions of A, B and C. I will present a very recent result concerning them. Also, it turns out that those operator integral mappings have interesting applications to perturbation theory for operators, that is, what could be for instance a Taylor formula when we replace real numbers by operators?
This is a joint work with Christian Le Merdy (University of Bourgogne - Franche-Comté) and Fedor Sukochev (UNSW, Sydney).
Contact Name: Anna Skripka