On $C$-compact orthogonally additive operators

N. A. Dzhusoeva, Z. S. Valgasov

North-Ossetian State University, 46 Vatutina str., Vladikavkaz, 362025 Russia

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 $E$.

Keywords: orthogonally additive operator, $C$-compact operator, $AM$-compact orthogonally additive map, Banach lattice, $AM$-space, lateral ideal.

UDC: 517.98:519.46

Received: 30.01.2024
Revised: 28.02.2024
Accepted: 20.03.2024

DOI: 10.26907/0021-3446-2025-2-29-38

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2025, 69:2, 24–31