9 papers
Relative uniform convergence and Archimedean property in pre-ordered vector spaces and abelian groups
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…
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…
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…
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…