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.
Information