Thermodynamics Research: Open Access(TROA)

Independent researcher, Spain

Publications

• Review Article   
  Weak and Weak* Operators in Non-Separable Banach Spaces: Topological Properties, Convergence and Structural Insights
  Author(s): Juan Alberto Molina Garcia*
  
  This article develops a rigorous framework for the study of weak and weak* operators in nonseparable Banach spaces (NSBS), where many of the foundational results of classical functional analysis fail or require significant reformulation. While the separable case is governed by compactness principles such as the Banach–Alaoglu theorem, the Eberlein– Šmulian theorem, and Rosenthal’s characterization of weakly compact sets, these rely heavily on metrizability and sequential compactness, both of which are absent in non-separable settings. Consequently, the extension of weak and weak* operator theory to NSBS is not straightforward and requires a careful topological re-evaluation. The main objective of this work is to provide generalized notions of weak compactness, weak*continuity, and convergence of operators in NSBS, formulated in terms of nets rather t.. Read More»
  

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