M. Marabeh

most citedOrder convergence in infinite-dimensional vector lattices is not topological

10 citations · 12 across the 4 of their papers we have counts for

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5 papers · 1 filter

math.FA2018

Brezis - Lieb spaces and an operator version of Brezis - Lieb's lemma

Eduard Emelyanov, Mohammad Marabeh

The Brezis - Lieb spaces, in which Brezis - Lieb's lemma holds true for nets, are introduced and studied. An operator version of Brezis - Lieb's lemma is also investigated.

math.FA2017

$u m$ -Topology in multi-normed vector lattices

Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh

Let $M = {m_{λ}}_{λ \in Λ}$ be a separating family of lattice seminorms on a vector lattice $X$ , then $(X, M)$ is called a multi-normed vector lattice (or MNVL). We…

math.FA2017

$uτ$ -Convergence in locally solid vector lattices

Y. A. Dabboorasad, E. Yu. Emelyanov, M. A. A. Marabeh

Let $x_{α}$ be a net in a locally solid vector lattice $(X, τ)$ ; we say that $x_{α}$ is unbounded $τ$ -convergent to a vector $x \in X$ if $∣ x_{α} - x ∣ \land w τ 0$ fo…

math.FA2017★ 10 cited

Order convergence in infinite-dimensional vector lattices is not topological

Y. A. Dabboorasad, E. Y. Emelyanov, M. A. A. Marabeh

In this note, we show that the order convergence in a vector lattice $X$ is not topological unless $dim X < \infty$ . Furthermore, we show that, in atomic order continuous Banach lat…

math.FA2017★ 2 cited

Compact-Like Operators in Lattice-Normed Spaces

A. Aydın, E. Yu. Emelyanov, N. Erkurşun Özcan +1

A linear operator $T$ between two lattice-normed spaces is said to be $p$ -compact if, for any $p$ -bounded net $x_{α}$ , the net $T x_{α}$ has a $p$ -convergent subnet. $p$ -Compact operato…