Matrix Limit Theorems of Kato Type Related to Positive Linear Maps and Operator Means
We obtain limit theorems for \(\Phi (A^p)^{1/p}\) and \((A^p\sigma B)^{1/p}\) as \(p\rightarrow \infty \) for positive matrices A, B, where \(\Phi \) is a positive linear map between matrix algebras (in particular, \(\Phi (A)=KAK^*\) ) and \(\sigma \) is
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Themistocles M. Rassias Valentin A. Zagrebnov Editors
Analysis and Operator Theory Dedicated in Memory of Tosio Kato’s 100th Birthday Foreword by Barry Simon
Springer Optimization and Its Applications Volume 146 Managing Editor Panos M. Pardalos
(University of Florida)
Honorary Editor Ding-Zhu Du (University of Texas at Dallas) Advisory Editors J. Birge, Booth School of Business (University of Chicago) S. Butenko, Department of Industrial and Systems Engineering (Texas A & M University) F. Giannessi, Dipto. Matematica (University of Pisa) S. Rebennack, Institute of Operations Research (Karlsruhe Institute of Technology) T. Terlaky, Department of Industrial and Systems Engineering (Lehigh University) Y. Ye, Department of Engineering (Stanford University)
Aims and Scope Optimization has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time, one of the most striking trends in optimization is the constantly increasing emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in all areas of applied mathematics, engineering, medicine, economics and other sciences. The series Springer Optimization and Its Applications publishes undergraduate and graduate textbooks, monographs and state-of-the-art expository works that focus on algorithms for solving optimization problems and also study applications involving such problems. Some of the topics covered include nonlinear optimization (convex and nonconvex), network flow problems, stochastic optimization, optimal control, discrete optimization, multi-objective programming, description of software packages, approximation techniques and heuristic approaches.
More information about this series at http://www.springer.com/series/7393
Themistocles M. Rassias Valentin A. Zagrebnov
•
Editors
Analysis and Operator Theory Dedicated in Memory of Tosio Kato’s 100th Birthday
Foreword by Barry Simon, IBM Professor of Mathematics and Theoretical Physics, Emeritus; California Institute of Technology, Pasadena, CA 91125, USA
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Editors Themistocles M. Rassias National Technical University of Athens Zografou Campus Athens, Greece
Valentin A. Zagrebnov Institute of Mathematics Aix-Marseille University Marseille, France
ISSN 1931-6828 ISSN 1931-6836 (electronic) Springer Optimization and Its Applications ISBN 978-3-030-12660-5 ISBN 978-3-030-12661-2 (eBook) https://doi.org/10.1007/978-3-030-12661-2 Library of Congress Control Number: 2019930373 Mathematics Subject Classification (2010): 46L80, 47A58, 46Txx, 00A79 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on
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