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.References
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Additional Information
- 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
- 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 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 111-119
- MSC (1991): Primary 47A35, 47B15, 47B44
- DOI: https://doi.org/10.1090/S0002-9939-97-03504-1
- MathSciNet review: 1343708