Convergence theorems and Tauberian theorems for functions and sequences in Banach spaces and Banach lattices |
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| Authors: | Yuan-Chuan Li Ryotaro Sato Sen-Yen Shaw |
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| Institution: | (1) Department of Applied Mathematics, National Chung-Hsing University, Taichung, 402, Taiwan;(2) Department of Mathematics, Okayama University, Okayama 700-8530, Japan;(3) Graduate School of Engineering, Lunghwa University of Science and Technology, Gueishan, Taoyuan, 333, Taiwan |
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| Abstract: | We prove generalized convergence theorems and Tauberian theorems for vector-valued functions and sequences of growth order
γ − 1 with γ > 0 and for positive functions and sequences in Banach lattices. Then the general results are applied to obtain
some interesting particular Tauberian results for various examples of operator semigroups. Among them are mean ergodic theorems
for Cesàro-mean-bounded semigroups (discrete and continuous) of operators and for semigroups of positive operators.
Research supported in part by the National Science Council of Taiwan.
Current address: 19-18, Higashi-hongo 2-chome, Midori-ku, 226-0002 Japan. |
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