The convergence on algebraic lattice normed spaces

Abstract

The multiplicative convergence on Riesz algebras introduced and investigated with respect to norm and order convergences. If is a Riesz space E and is a Riesz algebra then the vector norm mu: X -> E+ can be considered. Then (X, mu, E) is called algebraic lattice normed spaces. A net (x(alpha))(alpha is an element of A) in an (X, mu, E) is said to be multiplicative mu-convergent to x is an element of X if mu(x(alpha) - x).u ->(o) 0 holds for all u is an element of E+. In this paper, the general properties of this convergence are studied.