Abstract
The Hahn–Banach theorem is one of the major theorems proved in any first course on functional analysis. It has plenty of applications, not only within the subject itself, but also in other areas of mathematics like optimization, partial differential equations, and so on. This article will give a brief overview of the Hahn–Banach theorem, its ramifications and indicate some applications.
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Suggested Reading
W Rudin, Functional Analysis, McGraw-Hill, 1973.
S Kesavan, Nonlinear Functional Analysis: A First Course, Texts and readings in Mathematics (TRIM), 28, Hindustan Book Agency, 2004.
S Kesavan, Topics in Functional Analysis and Applications, New Age International (P) Limited (originally Wiley-Eastern), 1989.
P G Ciarlet, Introduction à l’analyse numérique matricielle et à l’optimisation, Masson, Paris, France, 1982; English translation, Cambridge University Press, Cambridge, UK, 1989.
S Kesavan, Functional Analysis, Texts and readings in Mathematics (TRIM), 52, Hindustan Book Agency, 2009.
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S Kesavan is Adjunct Professor at the Indian Institute of Technology, Madras. His area of interest is partial differential equations with specialization in elliptic problems connected to homogenization, control theory and isoperimetric inequalities. He has authored four books covering topics in functional analysis and its applications to partial differential equations.
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Kesavan, S. On the Hahn–Banach theorem. Reson 22, 915–933 (2017). https://doi.org/10.1007/s12045-017-0552-4
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DOI: https://doi.org/10.1007/s12045-017-0552-4