| dc.description | The main question of the thesis is the following: given a C*-algebra ${\cal A}$ which elements of ${\cal A}$ can be factored as, or approximated by, finite products of positive operators, with each factor also from ${\cal A}$? We begin by extending Ballantine's theorem for matrices to the class of n-normal operators. This introduces measure theory, while in another direction we obtain approximation theorems for AF-algebras. Combining AF-algebras with n-normal operators we obtain Approximately Poly-Normal Algebras (APN) and give a characterization of those APN-algebras for which the set of products of four positive operators is dense. We conclude with partial results on the "direct integral" and the "compact direct integral", two algebras which arise in a natural way from a "measurable field of C*-algebras". | en_US |
