Order projection in $\mathcal{OA}_r(E,F)$
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 407-423.

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We investigate order projections onto different bands in the space of all regular orthogonally additive operators. In particular, we obtain formulas for calculation of the order projections onto the band generated by a directed set of positive orthogonally additive operators and onto the band of all laterally continuous operators.
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N. A. Dzhusoeva; S. Yu. Itarova; M. A. Pliev. Order projection in $\mathcal{OA}_r(E,F)$. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 68 (2022) no. 3, pp. 407-423. http://geodesic.mathdoc.fr/item/CMFD_2022_68_3_a1/

[1] Abasov N. M., “O summe uzkikh ortogonalno additivnykh operatorov”, Izv. vuzov. Ser. Mat., 64:7 (2020), 3–9 | MR | Zbl

[2] Kolesnikov E. V., “Razlozhenie polozhitelnogo operatora”, Sib. mat. zh., 30:5 (1989), 77–79 | MR | Zbl

[3] Kolesnikov E. V., “Neskolko poryadkovykh proektorov, porzhdennykh idealami vektornoi reshetki”, Sib. mat. zh., 36:6 (1995), 1342–1349 | MR | Zbl

[4] Kolesnikov E. V., “V teni polozhitelnogo operatora”, Sib. mat. zh., 37:3 (1996), 592–598 | MR | Zbl

[5] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[6] Kusraev A. G., Mazhoriruemye operatory, Nauka, M., 2003 | MR

[7] Kusraev A. G., Kutateladze S. S., Vvedenie v bulevoznachnyi analiz, Nauka, M., 2005 | MR

[8] Kutateladze S. S., “Ob oskolkakh polozhitelnykh operatorov”, Sib. mat. zh., 30:5 (1989), 111–119 | MR | Zbl

[9] Pliev M. A., Popov M. M., “O prodolzhenii abstraktnykh operatorov Urysona”, Sib. mat. zh., 57:3 (2016), 700–708 | MR | Zbl

[10] Abasov N., “Completely additive and C-compact operators in lattice-normed spaces”, Ann. Funct. Anal., 11:4 (2020), 914–928 | DOI | MR | Zbl

[11] Abasov N., “On band preserving orthogonally additive operators”, Sib. Èlektron. Mat. Izv., 18:1 (2021), 495–510 | DOI | MR | Zbl

[12] Abasov N., “On a band generated by a disjointness dreserving orthogonally additive operator”, Lobachevskii J. Math., 42:5 (2021), 851–856 | DOI | MR | Zbl

[13] Abasov N., Pliev M., “On extensions of some nonlinear maps in vector lattices”, J. Math. Anal. Appl., 455:1 (2017), 516–527 | DOI | MR | Zbl

[14] Aliprantis C., Burkinshaw O., “The components of the positive operator”, Math. Z., 185 (1983), 245–257 | DOI | MR

[15] Aliprantis C., Burkinshaw O., “Projecting onto the band of kernel operators”, Houston J. Math., 11:1 (1985), 7–13 | MR | Zbl

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

[17] Appell J., Zabrejko P. P., Nonlinear superposition operators, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl

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

[19] Erkursun Ozcan N., Pliev M., “On orthogonally additive operators in $C$-complete vector lattices”, Banach J. Math. Anal., 16:1 (2022), 6 | DOI | MR | Zbl

[20] Feldman W. A., “A factorization for orthogonally additive operators on Banach lattices”, J. Math. Anal. Appl., 472:1 (2019), 238–245 | DOI | MR | Zbl

[21] Fotiy O., Gumenchuk A., Krasikova I., Popov M., “On sums of narrow and compact operators”, Positivity, 24:1 (2012), 69–80 | DOI | MR

[22] Huijsmans C. B., de Pagter B., “Disjointness preserving and diffuse operators”, Compos. Math., 79 (1991), 351–374 | MR | Zbl

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

[24] Mazón J. M., Segura de León S., “Uryson operators”, Rev. Roumaine Math. Pures Appl., 35:5 (1990), 441–449 | MR

[25] Mykhaylyuk V., Pliev M., Popov M., “The lateral order on Riesz spaces and orthogonally additive operators”, Positivity, 25:2 (2021), 291–327 | DOI | MR | Zbl

[26] de Pagter B., “The components of a positive operator”, Indag. Math., 48 (1983), 229–241 | DOI | MR

[27] Pliev M., “On $C$-compact orthogonally additive operators”, J. Math. Anal. Appl., 494 (2021), 124594 | DOI | MR | Zbl

[28] Pliev M., Polat F., Weber M. R., “Narrow and $C$-compact orthogonally additive operators in lattice-normed spaces”, Results Math., 74:4 (2019), 157 | DOI | MR | Zbl

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

[30] Pliev M., Ramdane K., “Order unbounded orthogonally additive operators in vector lattices”, Mediterr. J. Math., 15:2 (2018), 55 | DOI | MR | Zbl

[31] Pliev M., Weber M. R., “Disjointness and order projections in the vector lattices of abstract Uryson operators”, Positivity, 20:3 (2016), 695–707 | DOI | MR | Zbl