Normalized system
From Encyclopedia of Mathematics
A system of elements of a Banach space whose norms are all equal to one, . In particular, a system of functions in the space is said to be normalized if
Normalization of a system of non-zero elements of a Banach space means the construction of a normalized system of the form , where the are non-zero numbers, the so-called normalizing factors. As a sequence of normalizing factors one can take .
References
[1] | S. Kaczmarz, H. Steinhaus, "Theorie der Orthogonalreihen" , Chelsea, reprint (1951) |
[2] | N. Dunford, J.T. Schwartz, "Linear operators. General theory" , 1 , Interscience (1958) |
[3] | L.V. Kantorovich, G.P. Akilov, "Functionalanalysis in normierten Räumen" , Akademie Verlag (1964) (Translated from Russian) |
How to Cite This Entry:
Normalized system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normalized_system&oldid=18213
Normalized system. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normalized_system&oldid=18213
This article was adapted from an original article by A.A. Talalyan (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article