| dc.description.abstract | The principal question discussed in this dissertation is the
problem of characterizing the existence of admissible Frechet differentiable
norms on Banach spaces.
In the first chapter the basic concepts of normed linear spaces
are introduced and a summary of differential calculus on Banach spaces
is given.
The following three chapters of the paper are concerned with the
existence of an admissible Frechet differentiable norm on a separable
Banach space. A construction of such a norm is given for a separable
space which has a separable dual. Also, it is shown that if such a
norm exists on a Banach space, then the density character of the space
equals the density character of its dual.
In Chapter V, it is shown that if the density characters of a
space and its dual are not equal, then the space admits a rough norm.
As a consequence of this, there is no Frechet differentiable function
on this space with bounded non-empty support. This implies that the
space does not admit a Frechet differentiable norm. | |
