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Approximately Linear Functionals on Hilbert Spaces

✍ Scribed by Peter Šemrl

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
147 KB
Volume
226
Category
Article
ISSN
0022-247X

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✦ Synopsis

Let H be a real or complex Hilbert space, and let ) 0. A functional f on H is < Ž . Ž . Ž .< called an -approximately linear functional if f x q y y f x y f y F Ž< < 5 5 < < 5 5.

x q y for all scalars , and all vectors x, y g H. If such a functional f is bounded then there exists a continuous linear functional g on H such < Ž . Ž .< 5 5 that f x y g x F 37 x for every x g H.

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