Ratio limit theorems and Tauberian theorems for vector-valued functions and sequences

摘要

We prove ratio limit theorems for (C, γ)-means (γ ≥ 0) and Abel means of functions and sequences in Banach spaces, and ratio Tauberian theorems for (C, γ)-means (γ ≥ 1) and Abel means of functions and sequences in Banach lattices.