Ratio Tauberian theorems for positive functions and sequences in Banach lattices. (English) Zbl 1127.40003
Summary: 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 counterexamples are given to show that the hypotheses in the ratio Tauberian theorems are essential.
MSC:
| 40E05 | Tauberian theorems |
| 40G05 | Cesàro, Euler, Nörlund and Hausdorff methods |
| 47A35 | Ergodic theory of linear operators |
| 47D06 | One-parameter semigroups and linear evolution equations |
Keywords:
Cesàro limit; Abel limit; ratio limit theorem; ratio Tauberian theorem; generalized Tauberian theoremReferences:
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