Analysis in Banach Spaces: Volume II: Probabilistic Methods and Operator Theory

Description

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations. Front Matter ....Pages i-xxiii Random sums (Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis)....Pages 1-52 Type, cotype, and related properties (Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis)....Pages 53-162 R-boundedness (Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis)....Pages 163-250 Square functions and radonifying operators (Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis)....Pages 251-358 The H∞-functional calculus (Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis)....Pages 359-478 Back Matter ....Pages 479-616