EMBEDDINGS OF NEAR VECTOR SPACES AND APPLICATIONS IN PRE-HILBERT SPACES, FILTRATIONS, MARTINGALES, AND METRIC SPACES.

In this paper we introduce a family of embeddings jn, n ≥ 2, of a near vector space into a vector space. We give some examples for such embeddings and show that jn's invariant metric on a near vector space S defines an isometry on the vector space Rn(S), and if S is a near vector lattice then jn's are join preserving on the vector lattices Rn(S). Finally, we will find applications of this embeddings in Hilbert spaces, filtrations, martingales, and metric spaces. [ABSTRACT FROM AUTHOR]