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We prove an abstract mean ergodic theorem and use it to show that if {An} 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 IIx+AyII > II x -2 \/IAxII IIyHI (x, y G 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.

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