Infinite tensor products of spatial product systems

摘要

The aim of this work is to define the infinite tensor product circle times(u)(i is an element of I) E-i of a countable family {Ei}(i is an element of I) of spatial product systems with respect to a family u = {u(i)}(i is an element of I) of normalized units, and to analyze the main properties of this construction. Among other things, we show that circle times(u)(i is an element of I) E-i is an amenable product system, respectively a product system of type I, providedthat every product system E-i is amenable, respectively of type I.