Geodesic
On extension of dominated Uryson operators
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 3-8 Cet article a éte moissonné depuis la source Math-Net.Ru

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We investigate the procedure of extension of a dominated orthogonally additive map dominated by a laterally continuous operator from laterally ideal to the whole space. It is established that such operator admits an extension that is dominated and laterally continuous. 
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N. M. Abasov; M. A. Pliev. On extension of dominated Uryson operators. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 1, pp. 3-8. http://geodesic.mathdoc.fr/item/VMJ_2016_18_1_a0/

[1] Mazón J. M., Segura de León S., “Order bounded orthogonally additive operators”, Rev. Roumaine Math. Pures Appl., 35:4 (1990), 329–353 | MR | Zbl

[2] Mazón J. M., Segura de León S., “Uryson operators”, Rev. Roumaine Math. Pures Appl., 35:5 (1990), 431–449 | MR | Zbl

[3] Kusraev A. G., Pliev M. A., “Ortogonalno additivnye operatory v reshetochno normirovannykh prostranstvakh”, Vladikavk. mat. zhurn., 1:3 (1999), 31–41 | MR | Zbl

[4] Kusraev A. G., Pliev M. A., “Slaboe integralnoe predstavlenie mazhoriruemogo ortogonalno additivnogo operatora”, Vladikavk. mat. zhurn., 1:4 (1999), 21–37 | MR | Zbl

[5] Pliev M. A., “Mazhoriruemye operatory Urysona v prostranstvakh so smeshannoi normoi”, Vladikavk. mat. zhurn., 9:3 (2007), 47–57 | MR | Zbl

[6] Abasov N., Pliev M., “Order properties of the space of dominated Uryson operators”, Int. J. of Math. Anal., 9:45 (2015), 2211–2219

[7] Ben Amor M. A., Pliev M., “Laterally continuous part of an abstract Uryson operator”, Int. J. of Math. Anal., 7:58 (2013), 2853–2860 | MR

[8] Getoeva A., Pliev M., “Domination problem for orthogonally additive operators in lattice-normed spaces”, Int. J. of Math. Anal., 9:27 (2015), 1341–1352

[9] Gumenchuk A. V., Pliev M. A., Popov M. M., “Extensions of orthogonally additive operators”, Math. Stud., 41:2 (2014), 214–219 | MR | Zbl

[10] Pliev M., Popov M., “Narrow orthogonally additive operators”, Positivity, 18:4 (2014), 641–667 | DOI | MR | Zbl

[11] Pliev M., Popov M., “Dominated Uryson operators”, Int. J. of Math. Anal., 8:22 (2014), 1051–1059

[12] Pliev M., “Domination problem for narrow orthogonally additive operators”, Positivity (to appear) | DOI

[13] Pliev M. A., Weber M. R., “Disjointness and order projections in the vector lattices of abstract Uryson operators”, Positivity (to appear) | DOI

[14] Kusraev A. G., Mazhoriruemye operatory, Nauka, M., 2003, 619 pp. | MR

[15] Aliprantis C. D., Burkinshaw O., Positive Operators, Springer, Dordrecht, 2006 | MR | Zbl