Takahiro Hasebe (Hokkaido University) : Lifting operators on a Hilbert space nicely to the tensor
product or free product Hilbert space
Abstract: The basic five notions of independences in noncommutative probability (tensor, free, boolean, monotone, antimonotone) have
canonical operator models on Hilbert spaces. All these models are based on constructing a « good composite Hilbert space » (mostly, the
tensor product or free product Hilbert spaces) and a « good lifting » of operators to the composite space. In classical probability, this
corresponds to the well known construction of independent random variables on the product of probability spaces. In this talk, we
axiomatize « good liftings » and classify them. The subsequent talk, given by Malte Gerhold, discusses applications to finding new
noncommutative independences for random vectors. This talk is based on a joint work with Malte Gerhold and Michael Ulrich.