Abstract
This chapter mainly provides technical background information. We start with the so-called Convergence Lemma (Section 5.1) and some fundamental boundedness and approximation results (Section 5.2). Then we prove equivalence of boundedness of F-functional calculi for different subalgebras F of H∞ (Section 5.3). We also introduce and study the H∞-angle (Section 5.4) and present permanence results with respect to additive perturbations (Section 5.5). Finally, we prove a technical lemma which indicates the connections with Harmonic Analysis (Section 5.6).
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© 2006 Birkhäuser Verlag
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Haase, M. (2006). The Boundedness of the H∞-Calculus. In: The Functional Calculus for Sectorial Operators. Operator Theory: Advances and Applications, vol 169. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7698-8_5
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DOI: https://doi.org/10.1007/3-7643-7698-8_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7697-0
Online ISBN: 978-3-7643-7698-7
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