Titlebook: Advanced Techniques with Block Matrices of Operators; Mohammad Sal Moslehian,Hiroyuki Osaka Book 2024 The Editor(s) (if applicable) and Th

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Heinrich Holland,Kurt Scharnbacherto represent an operator on a space using simpler operators on its specific subspaces. We provide an in-depth study of dilation theory and give several characterizations of the positivity of . operator matrices of the form .. We also investigate the properties of . matrices with entries in a .-algeb

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https://doi.org/10.1007/978-3-322-85680-7 both linear and nonlinear positive maps within the realm of .-algebras presents an intriguing challenge in operator theory and matrix analysis, finding applications in diverse fields such as statistics, quantum information, and mechanics.

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Heinrich Holland,Kurt ScharnbacherThis chapter is devoted to a comprehensive study of operator monotone and operator convex functions. We establish connections between operator monotone functions and operator means by employing the Kubo–Ando theory.

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Matrices and Hilbert Space Operators,We introduce basic concepts and key results from functional analysis, operator theory, and matrix analysis. These concepts and results will play a central role as indispensable tools in the upcoming chapters.

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,Operator Monotone Functions and Positive Maps,This chapter is devoted to a comprehensive study of operator monotone and operator convex functions. We establish connections between operator monotone functions and operator means by employing the Kubo–Ando theory.

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,Operator Variance and Covariance,In this chapter, we expand upon the concepts of variance and covariance, going beyond the boundaries of classical probability theory to operate within a noncommutative framework. Within this setting, we establish upper bounds for unitarily invariant norms associated with the covariance of bounded linear operators and matrices.