Juan Alberto Molina Garcia
Independent researcher, Spain
Publications
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Review Article
Approximate C∗- and W∗-Algebras on Non-Separable Banach Spaces: Structure, Positivity, and Representation Theory
Author(s): Juan Alberto Molina Garcia*
This paper develops a comprehensive algebraic framework for extending the classical theory of C∗ - and W∗ -algebras to non-separable Banach spaces. By constructing Approximate C∗ - and W∗-algebras, defined as directed inductive limits of local operator algebras acting on separable subspaces, we obtain a rigorous structure that preserves the essential algebraic, topological, and spectral properties of classical operator algebras while overcoming the limitations imposed by separability. The first part of the article establishes the fundamental definitions of approximate C∗ -algebras, including approximate positivity, involution stability, and norm consistency under directed limits of projections. We then formulate and prove an Approximate Gelfand–Naimark theorem, showing that every approximately self-adjoint algebra can be faithfully represented .. Read More»