Ratio Tauberian Theorems for Positive Functions and Sequences in Banach Lattices
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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.
Mathematics Subject Classification (2000)
40E05 40G05 47A35 47D06Keywords
Cesàro limit Abel limit ratio limit theorem ratio Tauberian theorem generalized Tauberian theoremPreview
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© Birkhäuser Verlag, Basel 2007