Dual spaces of certain vector sequence spaces

On the dual of certain locally convex function spaces

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.

Finite Vector Spaces and Certain Lattices

The Galois number Gn(q) is defined to be the number of subspaces of the n-dimensional vector space over the finite field GF (q). When q is prime, we prove that Gn(q) is equal to the number Ln(q) of n-dimensional mod q lattices, which are defined to be lattices (that is, discrete additive subgroups of n-space) contained in the integer lattice Z and having the property that given any point P in t...

on the dual of certain locally convex function spaces

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.

Some Basic Properties of Vector Sequence Spaces

Dual Vector Spaces and Scalar Products

Remember that any linear map is fully determined by its action on an (arbitrary) basis. In fact, for ~v = ∑ 1≤k≤n λk~vk one gets νi(~v) = λi ∈ R (i = 1, . . . , n). We prove that ν1, . . . , νn ∈ V ∗ are linearly independent. Assume that the vector α := ∑ 1≤k≤n μkνk ∈ V ∗ is the zero map. I.e. ν(~v) = 0 ∈ R holds for all ~v ∈ V . Since this holds for all ~v ∈ V , it follows that μ1 = μ2 = · · ·...