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

Abstract

To the memory of Sen-Yen ShawKeywords: γ -Cesàro mean Abel mean Ratio limit theorem Ratio Tauberian theorem 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) andAbel means of functions and sequences in Banach lattices.