Uniformly ergodic multioperators
Authors:
M. Mbekhta and F.-H. Vasilescu
Journal:
Trans. Amer. Math. Soc. 347 (1995), 1847-1854
MSC:
Primary 47A35; Secondary 47A13
DOI:
https://doi.org/10.1090/S0002-9947-1995-1273509-1
MathSciNet review:
1273509
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Abstract | References | Similar Articles | Additional Information
Abstract: A version of the uniform ergodic theorem valid for commuting multioperators is given.
- A. Brunel, Théorème ergodique ponctuel pour un semi-groupe commutatif finiment engendré de contractions de $L^{1}$, Ann. Inst. H. Poincaré Sect. B (N.S.) 9 (1973), 327–343 (French, with English summary). MR 0344415
- Nelson Dunford, Spectral theory. I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185–217. MR 8642, DOI https://doi.org/10.1090/S0002-9947-1943-0008642-1
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- Tosio Kato, Perturbation theory for linear operators, 2nd ed., Springer-Verlag, Berlin-New York, 1976. Grundlehren der Mathematischen Wissenschaften, Band 132. MR 0407617
- Ulrich Krengel, Ergodic theorems, De Gruyter Studies in Mathematics, vol. 6, Walter de Gruyter & Co., Berlin, 1985. With a supplement by Antoine Brunel. MR 797411
- Michael Lin, On the uniform ergodic theorem, Proc. Amer. Math. Soc. 43 (1974), 337–340. MR 417821, DOI https://doi.org/10.1090/S0002-9939-1974-0417821-6
- Mostafa Mbekhta and Jaroslav Zemánek, Sur le théorème ergodique uniforme et le spectre, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 12, 1155–1158 (French, with English and French summaries). MR 1257230
- Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, DOI https://doi.org/10.1016/0022-1236%2870%2990055-8
- Joseph L. Taylor, The analytic-functional calculus for several commuting operators, Acta Math. 125 (1970), 1–38. MR 271741, DOI https://doi.org/10.1007/BF02392329
- Florian-Horia Vasilescu, Analytic functional calculus and spectral decompositions, Mathematics and its Applications (East European Series), vol. 1, D. Reidel Publishing Co., Dordrecht; Editura Academiei Republicii Socialiste România, Bucharest, 1982. Translated from the Romanian. MR 690957
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Additional Information
Keywords:
average,
Cesàro quasi-boundedness
Article copyright:
© Copyright 1995
American Mathematical Society