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