Abstract
This chapter provides important classes of linear operators in Banach spaces. Each class plays a crucial role in the investigation of parabolic problems. For later application we will distinguish between injective and non-injective operators. It starts with the classes of pseudo-sectorial and sectorial operators which allow for a Dunford functional calculus. With R-boundedness from Chapter 3 at hand, the class of operators admitting an R-bounded H¥-calculus is discussed. This class is of particular interest in view of our purposes later on. We refer to [DHP03], [KW04], and [Haa06] for a deeper investigation of the different classes.
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© 2012 Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden
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Nau, T. (2012). Classes of operators and Dunford functional calculus. In: Lp-Theory of Cylindrical Boundary Value Problems. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-8348-2505-6_4
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DOI: https://doi.org/10.1007/978-3-8348-2505-6_4
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-8348-2504-9
Online ISBN: 978-3-8348-2505-6
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