Local structure of Riesz valued sequence spaces defined by an order -function. Issue 3 (4th March 2017) - Herawati, E.; Supama; Mursaleen, M.
Abstract : For a Riesz space E, we introduce E -valued sequence spaces generated by an order -function. It is proved that these spaces equipped with a Luxemburg norm are ideal Banach lattices. We also determine necessary and sufficient conditions so that the Luxemburg norm on these spaces has the -order continuous property. Finally, we present some criteria for strictly monotonicity, uniformly monotonicity and locally monotonicity of the spaces.