6533b831fe1ef96bd1298fde
RESEARCH PRODUCT
Infinite Dimensional Banach spaces of functions with nonlinear properties
Juan B. Seoane-sepúlvedaDomingo GarcíaManuel MaestreBogdan C. GrecuBogdan C. Grecusubject
Inverse function theoremMathematics::Functional AnalysisMathematics(all)Approximation propertyGeneral MathematicsMathematical analysisInfinite-dimensional vector functionEberlein–Šmulian theoremBanach manifold/dk/atira/pure/subjectarea/asjc/2600Interpolation spaceLp spaceC0-semigroupMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-05-01 |