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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Yuan-Chuan Li and Sen-Yen Shaw
Journal: Proc. Amer. Math. Soc. 125 (1997), 111-119
MSC (1991): Primary 47A35, 47B15, 47B44
MathSciNet review: 1343708
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Abstract | References | Similar Articles | Additional Information

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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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

DOI: http://dx.doi.org/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
Article copyright: © Copyright 1997 American Mathematical Society