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Rademacher bounded families of operators on $ L_1$


Authors: N. J. Kalton and T. Kucherenko
Journal: Proc. Amer. Math. Soc. 136 (2008), 263-272
MSC (2000): Primary 47D06, 46E30
DOI: https://doi.org/10.1090/S0002-9939-07-09046-6
Published electronically: October 5, 2007
MathSciNet review: 2350412
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Abstract: We give a characterization of R-bounded families of operators on $ L_1.$ We then use this result to study sectorial operators on $ L_1$. We show that if $ A$ is an R-sectorial operator on $ L_1$, then, for any $ \epsilon>0,$ there is an invertible operator $ U:L_1\to L_1$ with $ \Vert U-I\Vert<\epsilon$ such that for some strictly positive Borel function $ w$, $ U(\D(A))$ contains the weighted $ L_1$-space $ L_1(w).$


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Additional Information

N. J. Kalton
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Email: nigel@math.missouri.edu

T. Kucherenko
Affiliation: Department of Mathematics, University of California Los Angeles, Box 951555, Los Angeles, California 90095-1555
Email: tamara@math.ucla.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09046-6
Keywords: Sectorial operators, representation of regular operators, R-boundedness
Received by editor(s): September 21, 2005
Received by editor(s) in revised form: December 6, 2006, and December 13, 2006
Published electronically: October 5, 2007
Additional Notes: The authors acknowledge support from NSF grants DMS-0244515 and DMS-0555670
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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