Tauberian operators on spaces of integrable functions

Abstract

The set $\mathcal{T}$(L₁(m), Y) of tauberian operators from L₁(m), where (Ω, Σ, m) is a σ-finite measure space, deserves attention for two reasons. First, because the properties of $\mathcal{T}$(L₁(m), Y) are similar to those of Φ₊(L₁(m), Y); and second, because L₁(m) supports many tauberian operators which are not upper semi-Fredholm when m is not purely atomic measure.