1 citations · 2 across the 9 of their papers we have counts for
10 papers
Optimal range of Haar martingale transforms and its applications
Sergey Astashkin, Jinghao Huang, Marat Pliev +2
Let be the standard dyadic filtration on . Let be the conditional expectation from onto $\mathcal{F}…
Atomic operators in vector lattices
Ralph Chill, Marat Pliev
In this paper we introduce a new class of operators on vector lattices. We say that a linear or nonlinear operator from a vector lattice to a vector lattice is atomic i…
The Dodds-Fremlin type theorem for abstract Uryson operators
Vladimir Orlov, Marat Pliev, Dmitry Rode
We continue the investigation of abstract Uryson operators in vector lattices. Using the recently proved Up-and-down theorem for order bounded, orthogonally additive operators, we…
Narrow operators on lattice-normed spaces and vector measures
D. T. Dzadzaeva, M. A. Pliev
We consider linear narrow operators on lattice-normed spaces. We prove that, under mild assumptions, every finite rank linear operator is strictly narrow (before it was known that…
Domination Problem for Narrow Orthogonally Additive Operators
Marat A. Pliev
The "Up-and-down" theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result of the operator theory. We prove…
Decomposition of an abstract Uryson operator
M. A. Ben Amor, M. Pliev
We consider the space of abstract Uryson operators firstly introduced in [9]. We obtain the formulas for band projections on the band generated by increasing set of a positive Urys…
Dominated Uryson operators on lattice-normed spaces
Marat Pliev, Batradz Tasoev
The aim of this note is to introduce the space D_{U}(V,W) of the dominated Uryson operators on lattice-normed spaces. We prove an "Up-and-down" type theorem for a positive abstract…
Narrow operators on lattice-normed spaces
M. Pliev
The aim of this article is to extend results of Maslyuchenko O., Mykhaylyuk V. Popov M. about narrow operators on vector lattices. We give a new definition of a narrow operator whe…
Narrow orthogonally additive operators
Marat Pliev, Mikhail Popov
We extend the notion of narrow operators to nonlinear maps on vector lattices. The main objects are orthogonally additive operators and, in particular, abstract Uryson operators. M…
Stinespring type theorem for a finite family of maps on Hilbert C*-modules
Marat Pliev
The aim of this article is to extend the results of Asadi M.B, B.V.R. Bhat, G. Ramesh, K. Sumesh about completely positive maps on Hilbert C*-modules. We prove a Stinespring type t…