Functional bases of numerical analysis : Banach-Steinhaus theorem

Banach-Steinhaus theorem
Functional bases of numerical analysis

Author : Claude BREZINSKI

Publication date: April 10, 2013 | Lire en français

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3. Banach-Steinhaus theorem

Let X and Y be two Banach spaces and let T be a linear application from X into Y. Given the norm

‖ T ‖ = \sum_{{‖ x ‖}_{x} \leq 1} {‖ Tx ‖}_{Y}

the vector space $L (X, Y)$ of bounded linear applications

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Ongoing reading
Banach-Steinhaus theorem

(1) - BREZINSKI (C.) - Padé – Type Approximation and General Orthogonal Polynomials - ISNM, vol. 50, Birkhäuser-Verlag, Basel (1980).
(2) - BREZINSKI (C.) - Projection Methods for Systems of Equations - North-Holland, Amsterdam (1997).
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