Proceedings of the Centre for Mathematics and its Applications

A remark on the $H^\infty$-calculus

Nigel J. Kalton

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Abstract

If $A,B$ are sectorial operators on a Hilbert space with the same domain and range, and if $\parallel Ax \parallel \approx \parallel Bx \parallel$ and $\parallel A^{-1}x\parallel \approx \parallel B^{-1}x \approx$, then it is a result of Auscher, McIntosh and Nahmod that if $A$ has an $H^\infty$-calculus then so does $B$. On an arbitrary Banach space this is true with the additional hypothesis on B that it is almost R-sectorial as was shown by the author, Kunstmann and Weis in a recent preprint. We give an alternative approach to this result.

Article information

Source
CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics". Alan McIntosh and Pierre Portal, eds. Proceedings of the Centre for Mathematics and its Applications, v. 42. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 2007), 81-90

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416321169

Mathematical Reviews number (MathSciNet)
MR2328513

Zentralblatt MATH identifier
1160.47013

Citation

Kalton, Nigel J. A remark on the $H^\infty$-calculus. CMA/AMSI Research Symposium "Asymptotic Geometric Analysis, Harmonic Analysis and Related Topics", 81--90, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 2007. https://projecteuclid.org/euclid.pcma/1416321169


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