Some Theorems and Examples of Cone Banach Spaces

Abstract

In this paper, by defining a cone norm parallel to.parallel to(A) on E over itself which behaves like the absolute value norm on R, we construct examples of cone Banach spaces. Namely, we define the m-Euclidian cone normed space E(m), E(infinity) and the space C(E)(S) of continuous functions in cones, to generalize the Banach spaces R(m), l(infinity) and C [a, b], respectively. Some basic lemmas and theorems are also proved to help in the construction and in the proof of completeness of the above mentioned examples of cone normed spaces