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Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette Mar 2011

Formalizing Categorical And Algebraic Constructions In Operator Theory, William Benjamin Grilliette

Dissertations, Theses, and Student Research Papers in Mathematics

In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This modification allows clear definitions of a "relation" for generators of a C*-algebra and utilization of classical algebraic tools, such as Tietze transformations.