On the relationship between three classes of operators on Riesz spaces
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Publication:6261352
DOI10.2478/AWUTM-2019-0016arXiv1504.08016MaRDI QIDQ6261352
Publication date: 29 April 2015
Abstract: Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.
Linear operators on ordered spaces (47B60) Positive linear operators and order-bounded operators (47B65) Topological lattices (06B30) Ordered topological structures (06F30) Ordered topological linear spaces, vector lattices (46A40)
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