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Infinite dimensional Banach spaces of functions with nonlinear properties

✍ Scribed by D. García; B. C. Grecu; M. Maestre; J. B. Seoane-Sepülveda

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
151 KB
Volume
283
Category
Article
ISSN
0025-584X

No coin nor oath required. For personal study only.

✦ Synopsis

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R n failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

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