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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entitle

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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吞吞吐吐

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.

FACET

START

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.

文藝

,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.

變態(tài)

,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.