Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Keywords: Orthogonally additive operators, nonlinear integral opeartors, narrow operators, vector lattices, C*-algebras, completely positive maps
UDC: 517.98, 519.46

Subject:

Orthogonally additive operators in vector lattices and lattice-normed spaces, completely positive maps in C*-algebras

Main publications:

1. M. Pliev, F. Sukochev, “Orthogonally additive operators on complex vector lattices”, Journal of Mathematical Analysis and Applications, 541:2 (2025), 128719      
2. K. Kudaybergenov, M. Pliev, F. Sukochev, “Fragments of orthogonally additive operators and the nonlinear Dodds-Fremlin’s theorem”, Journal of Mathematical Analysis and Applications, 550:2 (2025), 129551    
3. N. Dzhusoeva, E. Grishenko, M. Pliev, F. Sukochev, “Narrow operators on C-complete lattice-normed spaces”, Nonlinear Analysis, 243 (2024), 113524      
4. M. Pliev, F. Sukochev, “Narrow operators on tensor products of Köthe spaces”, Journal of Mathematical Analysis and Applications, 522:1 (2023), 126950      
5. N. Dzhusoeva, M. S. Moslehian, M. Pliev, M. Popov, “Operators taking values in Lebesgue-Bochner spaces”, Proceedings of the American Mathematical Society, 151:8 (2023), 3493–3502    
6. N. Dzhusoeva, J. Huang, M. Pliev, F. Sukochev, “Lateral order on complex vector lattices and narrow operators”, Mathematische Nachrichten, 296:11 (2023), 5157–5170      
7. M. Pliev, M. Popov, “Representation theorems for regular operators”, Mathematische Nachrichten, 297:1 (2024), 126–143      
8. M. Pliev, “On C-compact orthogonally additive operators”, Journal of Mathematical Analysis and Applications, 494:1 (2021), 124594        
9. E. Basaeva, R. Kulaev, M. Pliev, “On orthogonally additive operators in Kothe-Bochner spaces”, Results in Mathematics, 76:1 (2021), 20      
10. M. Pliev, F. Sukochev, “The Kalton and Rosenthal type decomposition of operators in Kothe-Bochner spaces”, Journal of Mathematical Analysis and Applications, 500:2 (2021), 125142      
11. R. Chill, M. Pliev, “Atomic operators in vector lattices”, Mediterranean Journal of Mathematics, 17 (2020), 138      
12. M. Pliev, K. Ramdane, “Order unbounded orthogonally additive operators in vector lattices”, Mediterranean Journal of Mathematics, 15:2 (2018), 55        
13. M. Pliev, “Domination problem for narrow orthogonally additive operators”, Positivity, v.21, 1, (2017), pp. 23-33., 21:1 (2017), 23–33            
14. N. Abasov, M. Pliev, “On extensions of some nonlinear maps in vector lattices”, Journal of Mathematical Analysis and Applications, 455:1 (2017), 516–527      
15. M. Pliev, M. Popov, “Narrow orthogonally additive operators”, Positivity, 18:4 (2013), 641–667          

Full list of scientific publications

Personal pages:

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Organisations:

• North Caucasus Center for Mathematical Research VSC RAS
• North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz
• Vladikavkaz Scientific Centre of the Russian Academy of Sciences
• Peoples' Friendship University of Russia named after Patrice Lumumba, Moscow
• Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz