1 citations · 1 across the 13 of their papers we have counts for
14 papers
Relative uniform convergence and Archimedean property in pre-ordered vector spaces and Abelian groups
Ivan Emelyanenkov, Eduard Emelyanov
It is proved that, for a pre-ordered vector space , the quotient space is an Archimedeanization of , where is the closure of positive wedge in ru-topolo…
On automatic continuity of operators from ordered to topological vector spaces
Eduard Emelyanov, Svetlana Gorokhova
We study continuity and boundedness of order-to-topology bounded and order-to topology continuous operators from ordered to topological vector spaces. Several results on automatic…
Equi-bounded on order intervals families of semi-norms
Eduard Emelyanov
It is proved that equi-bounded on order intervals families of semi-norms on an ordered Banach space with a closed generating cone are equi-continuous.
On Levi operators between normed and vector lattices
Eduard Emelyanov
The notion of a Levi operator is an operator abstraction of the Levy property of a norm or, more generally of the Levi topology on a locally solid vector lattice. Various aspects o…
On automatic boundedness of some operators in ordered Banach spaces
Eduard Emelyanov
We study order-to-weak continuous operators from an ordered Banach space to a normed space. It is proved that under rather mild conditions every order-to-weak continuous operator i…
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…
On KB and Levi operators in Banach lattices
Eduard Emelyanov
We prove that an order continuous Banach lattice E is a KB-space if and only if each positive compact operator on E is a KB operator. We give conditions on quasi-KB (resp., quasi-L…
Operators Affiliated to Banach Lattice Properties and the Enveloping Norms
Eduard Emelyanov, Svetlana Gorokhova
Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford--Pettis operators, etc., through involving the Banach lattice structure. In the pr…