We prove some versions of Nikodym boundedness and Banach-Steinhaus-type theorems for Riesz space-valued measures and operators, and some convergence results connected with separability, in the setting of filter convergence. Among the used tools there are the positive regularity property of the Riesz space involved and the diagonal and block-respecting filters, which allow us to compare our settings with the corresponding classical ones.
Uniform boundedness principle, Banach-Steinhaus and approximation theorems for filter convergence in Riesz spaces
BOCCUTO, Antonio;
2012
Abstract
We prove some versions of Nikodym boundedness and Banach-Steinhaus-type theorems for Riesz space-valued measures and operators, and some convergence results connected with separability, in the setting of filter convergence. Among the used tools there are the positive regularity property of the Riesz space involved and the diagonal and block-respecting filters, which allow us to compare our settings with the corresponding classical ones.File in questo prodotto:
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