Blecher, David P.2013-12-022013-12-02August 2012013-08http://hdl.handle.net/10657/479Extension 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.application/pdfengThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).Operator algebrasExtensionsMathematics2013-12-02Thesisborn digital