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A branch of mathematics concerned with infinite dimensional spaces (mainly Function Spaces) and mappings between them. The Spaces may be of different, and possibly Infinite, Dimensions. These mappings are called Operators or, if the range is on the Real line or in the Complex Plane, Functionals.
See also Functional, Operator
References
Balakrishnan, A. V. Applied Functional Analysis, 2nd ed. New York: Springer-Verlag, 1981.
Berezansky, Y. M.; Us, G. F.; and Sheftel, Z. G. Functional Analysis, Vol. 1. Boston, MA: Birkhäuser, 1996.
Berezansky, Y. M.; Us, G. F.; and Sheftel, Z. G. Functional Analysis, Vol. 2. Boston, MA: Birkhäuser, 1996.
Birkhoff, G. and Kreyszig, E. ``The Establishment of Functional Analysis.'' Historia Math. 11, 258-321, 1984.
Hutson, V. and Pym, J. S. Applications of Functional Analysis and Operator Theory. New York: Academic Press, 1980.
Kreyszig, E. Introductory Functional Analysis with Applications. New York: Wiley, 1989.
Yoshida, K. Functional Analysis and Its Applications. New York: Springer-Verlag, 1971.
Zeidler, E. Nonlinear Functional Analysis and Its Applications. New York: Springer-Verlag, 1989.
Zeidler, E. Applied Functional Analysis: Applications to Mathematical Physics. New York: Springer-Verlag, 1995.