HLLY'S Theorem in Banach Lattice With order continuous norm in term of a double sequence

Abstract

In this paper, we introduce Helly and Helly -Bray theorems in term double sequence in the context of Riesz space with order continuous norm, and we review some of the results that are needed to prove our theorems.        

We state some definitions, like as the moment double sequence and complete moment. Later we prove the corresponding generalized moment theorem and representation in term of double sequence of positive operators.

2010 Mathematics Subject Classification primary 46B42.

Keywords: vector lattice, Moment sequence, completely moment sequence, positive operator.