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Relatively uniformly continuous semigroups on ordered vector spaces
Eduard Emelyanov, Nazife Erkursun-Ozcan, Svetlana Gorokhova
We study relatively uniformly continuous operator semigroups on ordered vector spaces and extend several recent results obtained by M. Kramar Fijavz, M. Kandic, M. Kaplin, and J. G…
On the extension of one-parameter operator semigroups to completions of Archimedean vector lattices
Eduard Emelyanov
Extensions of one-parameter operator semigroups on Archimedean vector lattices to their order/ru-completions are studied. Existence and uniqueness of the extension to the ru-comple…
Collective order boundedness of sets of operators between ordered vector spaces
Eduard Emelyanov, Nazife Erkursun-Ozcan, Svetlana Gorokhova
It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively…
On collectively -Levi sets of operators
Eduard Emelyanov
A collectively -Levi set of operators is a generalization of the -Levi operator. By use of collective order convergence, we investigate relations between collectively -Lev…
Collective order convergence and collectively qualified sets of operators
Eduard Emelyanov
Collective versions of order convergences and corresponding types of collectively qualified sets of operators in vector lattices are investigated. It is proved that collectively or…
On collectively almost (limitedly, order) L-weakly compact sets of operators
Safak Alpay, Eduard Emelyanov, Svetlana Gorokhova
We prove collective versions of semi-duality theorems for sets of almost (limitedly, order) L-weakly compact operators.
On collectively L-weakly compact sets of operators
Eduard Emelyanov
A set of bounded linear operators from a Banach space to a Banach lattice is collectively L-weakly compact whenever union of images of the unit ball is L-weakly compact. We extend…