Some stability theorems on narrow operators acting in L1 and C(K)

Анотація

A new proof of two stability theorems concerning narrow operators acting from L₁ to L₁ or from C(K) to an arbitrary Banach space is given. Namely a sum of two such operators and moreover a sum of a point-wise unconditionally convergent series of such operators is a narrow operator again. The relations between several possible definitions of narrow operators on L₁ are also discussed.