Juan Alberto Molina García
Independent researcher, Spain
Publications
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Review Article
Approximate Spectral Triples and Non-commutative Geometric Structures on Non-Separable Banach Spaces
Author(s): Juan Alberto Molina García*
This article develops a geometric extension of the approximate C^*- and W^*-algebra framework introduced in earlier work, showing that NSBS naturally give rise to noncommutative geometric structures in the sense of Connes. While classical noncommutative geometry is traditionally based on separable C^*-algebras and Hilbert spaces, many analytically relevant settings—such as l^∞, L^∞ (μ) for non-σ-finite measures, or C(βN)—lack separability and fall outside the scope of the usual spectral triple framework. The present work overcomes these limitations by developing a theory of approximate spectral triples, constructed as inductive limits of local spectral triples on separable components. Given a non-separable Banach space X, its approximate operator algebra A^approx (X) is defined as an inductive limit of separable C^*-algebras A_F. We show.. Read More»