Abstract
We prove two ratio Tauberian theorems and deduce two generalized Tauberian theorems for functions and sequences with values in positive cones of Banach lattices. Two counter-examples are given to show that the hypotheses in the ratio Tauberian theorems are essential.
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Li, YC., Sato, R. & Shaw, SY. Ratio Tauberian Theorems for Positive Functions and Sequences in Banach Lattices. Positivity 11, 433–447 (2007). https://doi.org/10.1007/s11117-007-2085-7
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DOI: https://doi.org/10.1007/s11117-007-2085-7