Bijective Disjointness Preserving Operators
A linear operator T: X → Y between vector lattices is said to be disjointness preserving if T sends disjoint elements in X to disjoint elements in Y. Let T: X → Y be a bijective disjointness preserving operator, and so the inverse operator T -1 exists. In this paper we discuss the most recent results regarding the following problem: when is T -1 disjointness preserving? Apart from presenting several counterexamples to this problem we also formulate many sufficient conditions for the affirmative answer to it.
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