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Summary
Most books on linear operators are not easy to follow for students and researchers without an extensive background in mathematics. Self-contained and using only matrix theory, Invitation to Linear Operators: From Matricies to Bounded Linear Operators on a Hilbert Space explains in easy-to-follow steps a variety of interesting recent results on linear operators on a Hilbert space. The author first states the important properties of a Hilbert space, then sets out the fundamental properties of bounded linear operators on a Hilbert space. The final section presents some of the more recent developments in bounded linear operators.
Author Biography
Takayuki Furuta is currently Professor of Applied Mathematics at the Science University of Tokyo, Japan
Table of Contents
| Hilbert Spaces | |
| Inner Product Spaces and Hilbert Spaces | p. 1 |
| Jordan-Neumann Theorem | p. 6 |
| Orthogonal Decomposition of Hilbert Space | p. 14 |
| Gram-Schmidt Orthonormal Procedure and Its Applications | p. 19 |
| Fundamental Properties of Bounded Linear Operators | |
| Bounded Linear Operators on a Hilbert Space | p. 32 |
| Partial Isometry Operator and Polar Decomposition of an Operator | p. 52 |
| Polar Decomposition of an Operator and Its Applications | p. 62 |
| Spectrum of an Operator | p. 79 |
| Numerical Range of an Operator | p. 91 |
| Relations among Several Classes of Non-normal Operators | p. 103 |
| Characterizations of Convexoid Operators and Related Examples | p. 107 |
| Further Development of Bounded Linear Operators | |
| Young Inequality and Holder-McCarthy Inequality | p. 122 |
| Lowner-Heinz Inequality and Furuta Inequality | p. 127 |
| Chaotic Order and the Relative Operator Entropy | p. 152 |
| Aluthge Transformation on p-Hyponormal Operators and log-Hyponormal Operators | p. 158 |
| A Subclass of Paranormal Operators Including log-Hyponormal Operators and Several Related Classes | p. 166 |
| Operator Inequalities Associated with Kantorovich Inequality and Holder-McCarthy Inequality | p. 188 |
| Some Properties on Partial Isometry, Quasinormality and Paranormality | p. 208 |
| Weighted Mixed Schwarz Inequality and Generalized Schwarz Inequality | p. 215 |
| Selberg Inequality | p. 218 |
| An Extension of Heinz-Kato Inequality | p. 223 |
| Norm Inequalities Equivalent to Lowner-Heinz Inequality | p. 226 |
| Norm Inequalities Equivalent to Heinz Inequality | p. 230 |
| Bibliography | p. 235 |
| Index | p. 247 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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