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An abstract ergodic theorem and some inequalities for operators on Banach spaces

Authors:	Yuan-Chuan Li Sen-Yen Shaw

Institution:	Department of Mathematics, National Central University, Chung-Li, Taiwan 320 ; Department of Mathematics, National Central University, Chung-Li, Taiwan 320

Abstract:	We prove an abstract mean ergodic theorem and use it to show that if $\{A_n\}$ 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 $\\|x+Ay\\|\ge \\|x\\|-2\sqrt {\\|Ax\\|\,\\|y\\|} (x,y\in D(A))$ holds for any -dissipative operator . These results either generalize or improve the corresponding results of Shaw, Mattila, and Crabb and Sinclair, respectively.

Keywords:	Abstract mean ergodic theorem hermitian operator hyponormal operator $m$-dissipative operator normal operator orthogonality strictly $c$-convex space

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