The Banach–Steinhaus Theorem

Alexander Kharazishvili
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Alexander Kharazishvili: Tbilisi State University, Andrea Razmadze Mathematical Institute

Chapter Chapter 11 in Lectures on Real-valued Functions, 2025, pp 105-112 from Springer

Abstract: Abstract As is mentioned in Dunford and Schwartz (Linear operators: general theory, Part 1. Wiley-Interscience, 1988), there are three fundamental principles of modern linear functional analysis: (i) the Hahn–Banach theorem on a continuous linear extension of a partial continuous linear functional; (ii) the Banach–Steinhaus theorem (also known as the principle of condensation of singularities); (iii) Banach’s theorem on open linear mappings (or on the closed graph of a linear mapping).

Date: 2025
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DOI: 10.1007/978-3-031-95369-9_11

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