Extensions of Approximately Unital Operator Algebras
Royce, Maureen 1952-
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Extension theory in the study of C*-algebras has been important in many aspects. For that reason, a theory of extensions of operator algebras, with as direct a link as possible to the C*-algebras theory, will be developed. In large part the theory will be developed via the natural C*-algebras generated by any operator algebra. The underlying structure used will be a generalization of Busby's theory of extensions of C*-algebras and results concerning universal completions for particular diagrams of Eilers, Loring, and Pedersen. Examples of our contributions as a result of this approach are a definition of the amalgamated free product of operator algebras, as well as a Tietze extension theorem for sigma-unital operator algebras.