ERRATUM TO: COMPACTNESS PROPERTIES FOR OPERATORS DOMINATED BY AM-COMPACT OPERATORS

摘要

In [3, Theorem 2.10] it was proposed to characterize Banach lattices such that operators dominated by AM-compact operators are AM-compact. But there was an error in the proof of the above-mentioned theorem. The purpose of this erratum is to give a new and correct proof of Theorem 2.10 of [3]. Let us recall that if Eis a Banach lattice, E' is its topological dual and φ, ∈ E', the null ideal of ψ, is defined by N_ψ, = {x ∈ : 1ψ1 (1x1) = 0} and the carrier C_ψ, of ψ∈ E' is defined by = N )~d = {u ∈ E :|U|=0 for all v ∈To give our proof, we will need the following lemma: