Juan Alberto Molina García
Independent researcher, Spain
Publications
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Research Article
Approximate Noncommutative Curvature, Index Theory, and Pseudodifferential Calculus on Non-Separable Banach Spaces
Author(s): Juan Alberto Molina García*
This article develops an analytic and geometric framework for approximate noncommutative curvature and index theory on non-separable Banach spaces (NSBS), extending classical operator-theoretic and pseudodifferential methods beyond the separability barrier. Motivated by the structural limitations of Banach spaces without countable Schauder bases, we construct a theory of approximate pseudodifferential operators (APDOs), defined through localised symbolic calculi on admissible nets rather than countable charts. A generalised approximate connection is introduced for operator modules over Banach–function algebras, enabling the definition of curvature-type quantities via commutator densities, asymptotic limits, and weakened continuity hypotheses compatible with non-separability. The main contribution is a comprehensive formulation of an approximate index theorem for Fredho.. Read More»