Local structure of Riesz valued sequence spaces defined by an order Phi-function

摘要

For a Riesz space E, we introduce E-valued sequence spaces generated by an order phi-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 sigma-order continuous property. Finally, we present some criteria for strictly monotonicity, uniformly monotonicity and locally monotonicity of the spaces.