Rademacher bounded families of operators on $L_1$
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- by N. J. Kalton and T. Kucherenko PDF
- Proc. Amer. Math. Soc. 136 (2008), 263-272 Request permission
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 $\|U-I\|<\epsilon$ such that for some strictly positive Borel function $w$, $U(\mathcal {D}(A))$ contains the weighted $L_1$-space $L_1(w).$References
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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
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2350412