Thermodynamics Research: Open Access(TROA)

Independent researcher, Spain

Publications

• Review Article   
  Operator Algebras on Non-Separable Banach Spaces and Applications in Mathematical Physics
  Author(s): Juan Alberto Molina Garcia*
  
  This paper develops a structural and functional framework for operator algebras acting on nonseparable Banach spaces (NSBS). While classical operator algebras—such as C∗ - and W∗ -algebras—are traditionally constructed on separable Hilbert spaces, many physical and mathematical contexts require non-separable or even transfinite structures: quantum field theories with infinitely many degrees of freedom, infinite tensor product systems, and algebras associated with non-measurable state spaces. We extend the classical operator-algebraic formalism to NSBS by introducing approximate operator algebras, defined through directed nets of weakly compact projections and local separable subspaces. This approach restores the analytic machinery of functional calculus, spectra, and representations, while preserving topological and dual properties within locally se.. Read More»
  

  Abstract HTML PDF