An abstract ergodic theorem and some inequalities for operators on Banach spaces |
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| Authors: | Yuan-Chuan Li Sen-Yen Shaw |
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| Affiliation: | Department of Mathematics, National Central University, Chung-Li, Taiwan 320 ; Department of Mathematics, National Central University, Chung-Li, Taiwan 320 |
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| Abstract: | We prove an abstract mean ergodic theorem and use it to show that if  is a sequence of commuting  -dissipative (or normal) operators on a Banach space  , then the intersection of their null spaces is orthogonal to the linear span of their ranges. It is also proved that the inequality  holds for any  -dissipative operator  . These results either generalize or improve the corresponding results of Shaw, Mattila, and Crabb and Sinclair, respectively. |
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| Keywords: | Abstract mean ergodic theorem hermitian operator hyponormal operator $m$-dissipative operator normal operator orthogonality strictly $c$-convex space. |
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