Some Results on Boundedness in Locally Convex Cones

The purpose of this paper is to introduce and to discuss the concept of p-approximation and p-orthogonality in vector spaces, and to obtain some results on p- orthogonality in vector spaces similar to some well known results on the orthogonality in normed spaces. We also discuss the concept of p-extension of linear functionals on a vector space, and give a characterization of linear functionals on a subspace having a unique p-extension Hahn-Banach to the whole vector space.