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Bibounded uo-convergence and b-property in vector lattices |
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| Authors: | Alpay Safak Emelyanov Eduard Gorokhova Svetlana |
| Institution: | 1.Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey ;2.Sobolev Institute of Mathematics, Novosibirsk, Russia, 630090 ;3.Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia, 362027 ; |
| Abstract: | We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system \(\langle X,X^{\sim }\rangle \), X has b-property if and only if the order convergence in X agrees with the order convergence in \(X^{\sim \sim }\). |
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