Proceedings of the American Mathematical Society

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

Author(s): Yuan-Chuan Li; Sen-Yen Shaw
Journal: Proc. Amer. Math. Soc. 125 (1997), 111-119.
MSC (1991): Primary 47A35, 47B15, 47B44
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A35, 47B15, 47B44

Yuan-Chuan Li
Affiliation: Department of Mathematics, National Central University, Chung-Li, Taiwan 320
Address at time of publication: Department of Mathematics, Chung Yuan University, Chung-Li, Taiwan 320

Sen-Yen Shaw
Affiliation: Department of Mathematics, National Central University, Chung-Li, Taiwan 320
Email: shaw@math.ncu.edu.tw

DOI: 10.1090/S0002-9939-97-03504-1
PII: S 0002-9939(97)03504-1
Keywords: Abstract mean ergodic theorem, hermitian operator, hyponormal operator, $m$-dissipative operator, normal operator, orthogonality, strictly $c$-convex space.
Received by editor(s): February 14, 1995
Received by editor(s) in revised form: May 18, 1995
Additional Notes: This research was supported in part by the National Science Council of the R.O.C
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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