Abstract
In Section 2.1 the basic theory of sectorial operators is developed, including examples and the concept of sectorial approximation. In Section 2.2 we introduce some notation for certain spaces of holomorphic functions on sectors. A functional calculus for sectorial operators is constructed in Section 2.3 along the lines of the abstract framework of Chapter 1. Fundamental properties like the composition rule are proved. In Section 2.5 we give natural extensions of the functional calculus to larger function spaces in the case where the given operator is bounded and/or invertible. In this way a panorama of functional calculi is developed. In Section 2.6 some mixed topics are discussed, e.g., adjoints and restrictions of sectorial operators and some fundamental boundedness and some first approximation results. Section 2.7 contains a spectral mapping theorem.
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© 2006 Birkhäuser Verlag
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Haase, M. (2006). The Functional Calculus for Sectorial Operators. 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_2
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DOI: https://doi.org/10.1007/3-7643-7698-8_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7697-0
Online ISBN: 978-3-7643-7698-7
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