Multiplicative order compact operators between vector lattices and Riesz algebras - Aydin, Abdullah; Gorokhova, Svetlana (Univ Nis, Fac Sci Math, 2024)
In this paper, we present and examine the concept of multiplicative order compact operators from vector lattices to Riesz algebras. Specifically, a linear operator T from a vector lattice X to an Riesz algebra E is deemed mmm-compact, if every net x(alpha) in an m-bounded subset of X possesses a subnet x alpha beta such that Tx(alpha beta) (mo)(->) y for some y E E. Moreover, we introduce and investigate mmm-M- and mmm-L-weakly compact operators.
Keywords: . Vector lattice; Riesz algebra; Multiplicative order compact operator; omo- M-Weakly compact operator; omo- L-Weakly compact operator