The Hahn–Banach Theorems and Weak Topologies

Fabio Botelho
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Fabio Botelho: Federal University of Pelotas, Department of Mathematics and Statistics

Chapter Chapter 2 in Functional Analysis and Applied Optimization in Banach Spaces, 2014, pp 41-56 from Springer

Abstract: Abstract Chapter 2 develops the concepts of weak topologies and weak convergence which are fundamental in the modern variational analysis. Many important problems are non-convex and have no minimizers in the classical sense. However the minimizing sequences in reflexive spaces may be weakly convergent, and it is important to evaluate the average behavior of such sequences in many practical applications.

Keywords: Weak Topology; Hahn-Banach Theorem; Modern Variational Analysis; Reflexive Space; Weak-star Compactness (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-06074-3_2

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DOI: 10.1007/978-3-319-06074-3_2

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