ALMOST EVERYWHERE CONVERGENCE OF GENERALIZED ERGODIC TRANSFORMS FOR INVERTIBLE POWER-BOUNDED OPERATORS IN LP

被引：4

作者：

Cuny, Christophe ^{[1
]}

机构：

[1] Ecole Cent Paris, Lab MAS, F-92295 Chatenay Malabry, France

来源：

COLLOQUIUM MATHEMATICUM | 2011年 / 124卷 / 01期

关键词：

Berkson-Gillespie spectral integral; L-P spaces; ergodic transforms; almost everywhere convergence; HILBERT TRANSFORM; THEOREM;

D O I：

10.4064/cm124-1-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L-2 (X, Sigma, mu) (mu is a sigma-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on L-P(X, Sigma, mu), p>1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.

引用

页码：61 / 77

页数：17

共 50 条

[1] ON THE ALMOST EVERYWHERE CONVERGENCE OF ERGODIC AVERAGES FOR POWER-BOUNDED OPERATORS ON LP-SUBSPACES
BERKSON, E
BOURGAIN, J
GILLESPIE, TA
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 1991, 14 (05) : 678 - 715
[2] Power-bounded Invertible Operators and Invertible Isometries on Lp Spaces
Gillespie, T. A.
[J]. OPERATOR SEMIGROUPS MEET COMPLEX ANALYSIS, HARMONIC ANALYSIS AND MATHEMATICAL PHYSICS, 2015, 250 : 241 - 252
[3] POWER-BOUNDED OPERATORS WITH INVERTIBLE CHARACTERISTIC FUNCTION
GHATAGE, P
[J]. ACTA SCIENTIARUM MATHEMATICARUM, 1975, 37 (3-4): : 201 - 204
[4] ON POWER-BOUNDED OPERATORS AND THE POINTWISE ERGODIC PROPERTY
FEDER, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 83 (02) : 349 - 353
[5] ALMOST EVERYWHERE CONVERGENCE OF ERGODIC AVERAGES OF NONLINEAR OPERATORS
WITTMANN, R
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1995, 127 (02) : 326 - 362
[6] On the maximal quadratic function for power-bounded operators in Lp
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[J]. MATHEMATICAL NOTES, 2000, 67 (5-6) : 802 - 805
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[8] ERGODIC POWER FUNCTIONS FOR MEAN BOUNDED, INVERTIBLE, POSITIVE OPERATORS
MARTINREYES, FJ
SALVADOR, PO
[J]. STUDIA MATHEMATICA, 1988, 91 (02) : 131 - 139
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[10] ON THE ALMOST EVERYWHERE CONVERGENCE OF THE ERGODIC AVERAGES
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DELATORRE, A
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1990, 10 : 141 - 149

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