However, the general concept of a functional had previously been introduced in 1887 by the Italian mathematician and physicist Vito Volterra.

The term was first used in Hadamard's 1910 book on that subject.

In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The theorem was first published in 1927 by Stefan Banach and Hugo Steinhaus but it was also proven independently by Hans Hahn. Theorem (Uniform Boundedness Principle).

E.: Functional Analysis, Theory and Applications, Hold, Rinehart and Winston, 1965. Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: Functional Analysis: An Introduction, American Mathematical Society, 2004. Friedman, A.: Foundations of Modern Analysis, Dover Publications, Paperback Edition, July 21, 2010 Giles,J.R.: Introduction to the Analysis of Normed Linear Spaces,Cambridge University Press,2000 Hirsch F., Lacombe G.

Online (by subscription) Bachman, G., Narici, L.: Functional analysis, Academic Press, 1966.

Herget: Applied Algebra and Functional Analysis, Dover, 1993. Pietsch, Albrecht: History of Banach spaces and linear operators, Birkhäuser Boston Inc., 2007, Reed, M., Simon, B.: "Functional Analysis", Academic Press 1980. Riesz, F.

Volume 38, North-Holland Mathematical Library, 1987, Brezis, H.: Analyse Fonctionnelle, Dunod or Conway, J.

Herget: Applied Algebra and Functional Analysis, Dover, 1993. Pietsch, Albrecht: History of Banach spaces and linear operators, Birkhäuser Boston Inc., 2007, Reed, M., Simon, B.: "Functional Analysis", Academic Press 1980. Riesz, F.

B.: A Course in Functional Analysis, 2nd edition, Springer-Verlag, 1994, Dunford, N.

and Vorovich, I.I.: Functional Analysis in Mechanics, Springer-Verlag, 2002 Michel, Anthony N.

E.: Functional Analysis, Theory and Applications, Hold, Rinehart and Winston, 1965. Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: Functional Analysis: An Introduction, American Mathematical Society, 2004. Friedman, A.: Foundations of Modern Analysis, Dover Publications, Paperback Edition, July 21, 2010 Giles,J.R.: Introduction to the Analysis of Normed Linear Spaces,Cambridge University Press,2000 Hirsch F., Lacombe G.

Israel Gelfand, to include most types of representation theory. ==See also== List of functional analysis topics Spectral theory ==References== ==Further reading== Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis: A Hitchhiker's Guide, 3rd ed., Springer 2007, .

Herget: Applied Algebra and Functional Analysis, Dover, 1993. Pietsch, Albrecht: History of Banach spaces and linear operators, Birkhäuser Boston Inc., 2007, Reed, M., Simon, B.: "Functional Analysis", Academic Press 1980. Riesz, F.

E.: Functional Analysis, Theory and Applications, Hold, Rinehart and Winston, 1965. Eidelman, Yuli, Vitali Milman, and Antonis Tsolomitis: Functional Analysis: An Introduction, American Mathematical Society, 2004. Friedman, A.: Foundations of Modern Analysis, Dover Publications, Paperback Edition, July 21, 2010 Giles,J.R.: Introduction to the Analysis of Normed Linear Spaces,Cambridge University Press,2000 Hirsch F., Lacombe G.

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