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.
KeywordsVector Lattice Banach Lattice Compact Hausdorff Space Nonzero Ideal Weighted Composition Operator
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