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 .
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Normalized system. A.A. Talalyan (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Normalized_system&oldid=18213