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Inductive and projective limits of Banach spaces of measurable functions with order unities with respect to power parameter
Authors
Eskandarian Z.
Novikov A.
Publication date
1 January 2016
Publisher
Abstract
© 2016, Allerton Press, Inc.We prove that a measurable function f is bounded and invertible if and only if there exist at least two equivalent norms by order unit spaces with order unities fα and fβ with α > β > 0. We show that it is natural to understand the limit of ordered vector spaces with order unities fα (α approaches to infinity) as a direct sum of one inductive and one projective limits. We also obtain some properties for the corresponding limit topologies
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Last time updated on 07/05/2019