0000000000774810
AUTHOR
Bogdan C. Grecu
Infinite Dimensional Banach spaces of functions with nonlinear properties
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.
Two-dimensional Banach spaces with polynomial numerical index zero
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Polynomial numerical indices of 𝐶(𝐾) and 𝐿₁(𝜇)
We estimate the polynomial numerical indices of the spaces C ( K ) C(K) and L 1 ( μ ) L_1(\mu ) .