Algebry operatorów i ich zastosowania w fizyce

The Choi-Effros product, granting the fixed point space of a unital completely positive map a unique von Neumann algebra structure is the key tool in the construction of the abstract Poisson boundary, generalising the classical concept of a probabilistic-type boundary for a random walk. In this talk we will discuss how replacing the completely positive map by a completely contractive one leads instead to a construction of a (weak*-closed) ternary ring of operators and present some applications to the study of fixed point spaces of contractive convolution operators on classical and quantum locally compact groups.(Mainly based on joint work with Pekka Salmi, Matthias Neufang and Nico Spronk)