Department of Mathematics
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o tau-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces
Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2022-06-01)
We investigate o tau-continuous/bounded/compact and Lebesgue operators from vector lattices to topological vector spaces; the Kantorovich-Banach operators between locally solid lattices and topological vector spaces; and t...
Full lattice convergence on Riesz spaces
Aydın, Abdullah; Emelyanov, Eduard; Gorokhova, Svetlana (2021-05-01)
The full lattice convergence on a locally solid Riesz space is an abstraction of the topological, order, and relatively uniform convergences. We investigate four modifications of a full convergence c on a Riesz space. The ...
Bibounded uo-convergence and b-property in vector lattices
Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2021-01-01)
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 ⟨ X, X∼⟩ , X has b-property if and only if the ord...
Unbounded p-Convergence in Lattice-Normed Vector Lattices
Aydın, A.; Emelyanov, Eduard; Erkurşun-Özcan, N.; Marabeh, M. (2019-07-01)
A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| xα− x| ∧ u) → o 0 for every u ∈ X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name...
u tau-convergence in locally solid vector lattices
Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (Springer Science and Business Media LLC, 2018-09-01)
Let be a net in a locally solid vector lattice ; we say that is unbounded -convergent to a vector if for all . In this paper, we study general properties of unbounded -convergence (shortly -convergence). -convergence gener...
Komls properties in Banach lattices
Emelyanov, Eduard; Gorokhova, S. G. (2018-08-01)
Several Komls like properties in Banach lattices are investigated. We prove that C(K) fails the -pre-Komls property, assuming that the compact Hausdorff space K has a nonempty separable open subset U without isolated point...
um-Topology in multi-normed vector lattices
Dabboorasad, Y. A.; Emelyanov, Eduard; Marabeh, M. A. A. (2018-04-01)
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) ...
Archimedean Cones in Vector Spaces
Emelyanov, Eduard (2017-01-01)
In the case of an ordered vector space (briefly, OVS) with an order unit, the Archimedeanization method was recently developed by Paulsen and Tomforde [4]. We present a general version of the Archimedeanization which cover...
Nonstandard hulls of ordered vector spaces
Emelyanov, Eduard (2016-06-01)
This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach sp...
Asymptotically absorbing nets of positive operators
Emelyanov, Eduard (2012-10-01)
This paper is devoted to asymptotically absorbing operator nets. The study of such nets has attracted an attention in [19, 20] in connection with the notion of the Lotz - Räbiger nets on a Banach space which had been studi...
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