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This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and LittlewoodPaley Theory. It presents a thorough study of the fundamental randomisation techniques and the operatortheoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, Kconvexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of Rboundedness 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 bisectorial 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 operatortheoretic approach to deterministic and stochastic evolution equations.
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