ABSTRACT
The preliminary results of the calculation of Banach algebra having been disposed of, one can begin the construction which will associate a Borel measure on the quasi-dual of a separable involutive Banach algebra to each representation of that algebra on a separable Hilbert space. This chapter relates the Mackey Borel structures and the Borel measures on the dual and the quasi–dual of a separable involutive Banach algebra to the representation theory of that algebra are largely due to Mackey and Ernest. Canonical measures were introduced by Ernest by means of a definition slightly different from the one employed. The problem of characterizing the canonical measures among all of the standard Borel measures.
