Unitary equivalence of spectral measures on a Baer -semigroup

Abstract

This paper is concerned with a generalization of the concept of unitary equivalence of spectral measures on a Baer *-semigroup. A connection is made between abstract spectral measures, and three other distinct mathematical systems.

Chapter II is devoted specifically to generalizing the concept of a spectral measure and to determining necessary and sufficient conditions for which two spectral measures will be unitarily equivalent.

Chapter III discusses the problem of each (C(M) , qμ) being type I in terms of cycles, the basic elements of C(M).

In Chapter IV it is shown that in a Loomis *-semigroup each type I (C(M) , qμ) will be type I homogeneous.

Chapter V relates the study of unitary equivalence of spectral measures and the unitary equivalence of normal elements in a Finite Dimensional Baer *-algebra.