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On C-compact orthogonally additive operators
https://doi.org/10.26907/0021-3446-2025-2-29-38
Abstract
It is shown that the set of all C-compact orthogonally additive operators from a vector lattice E to an AM-space F is a vector lattice and the lattice operations can be calculated by the Riesz–Kantorovich formulas. Moreover, a positive AM-compact orthogonally additive map defined on a lateral ideal of a vector lattice E and taking values in an AM-space F can be extended to the whole space E.
About the Authors
N. A. Dzhusoeva
North-Ossetian State University
Russian Federation
Russian Federation
Nonna A. Dzhusoeva.
46 Vatutina str., Vladikavkaz, 362025
Z. S. Valgasov
North-Ossetian State University
Russian Federation
Russian Federation
Zaurbek S. Valgasov.
46 Vatutina str., Vladikavkaz, 362025
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Review
For citations:
Dzhusoeva N.A., Valgasov Z.S. On C-compact orthogonally additive operators. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;(2):29-38. (In Russ.) https://doi.org/10.26907/0021-3446-2025-2-29-38
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