Type of Document	Dissertation
Author	Garren, Kenneth Ross
URN	etd-06022010-020328
Title	Unitary equivalence of spectral measures on a Baer -semigroup.
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title Bevis, Jean H. Committee Chair DePree, John D. Committee Member Johnson, Harry Lee Committee Member Rutland, Leon W. Committee Member
Keywords	Group theory
Date of Defense	1968-05-05
Availability	restricted
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.
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