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

Li, Yuan-Chuan; Shaw, Sen-Yen

doi:10.1090/S0002-9939-97-03504-1

An abstract ergodic theorem and some inequalities for operators on Banach spaces
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by Yuan-Chuan Li and Sen-Yen Shaw PDF

Proc. Amer. Math. Soc. 125 (1997), 111-119 Request permission

Abstract:

We prove an abstract mean ergodic theorem and use it to show that if $\{A_n\}$ is a sequence of commuting $m$-dissipative (or normal) operators on a Banach space $X$, 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 $m$-dissipative operator $A$. These results either generalize or improve the corresponding results of Shaw, Mattila, and Crabb and Sinclair, respectively.

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