Invitation to Linear Operators

From Matricies to Bounded Linear Operators on a Hilbert Space

Furuta Takayuki

254 pages, parution le 19/02/2002

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Résumé

Invitation to Linear Operators is an essential guide to linear operators. Linear operator theory is a natural extension of matrix theory. Most of the books on linear operators are not easy to read for students and researchers who have insufficient knowledge of mathematics. This book explains, in easy to follow steps, the newest essential and fundamental results on linear operators based on matrix theory. The topics covered include: Hilbert spaces, fundamental properties of bounded linear operators, and further developments of bounded linear operators. This book will undoubtedly be of interest to undergraduate and graduate students as well as researchers who have an interest in linear operators and their various applications. It also serves as a reference book for advanced readers.

Contents

1. Hilbert Spaces

1.1 Inner Product Spaces and Hilbert Spaces
1.2 Jordan-Neuman Theorem
1.3 Orthogonal Decomposition of Hilbert Space
1.4 Gram-Schmidt Orthonormal Procedure and its Applications

2. Fundamental Properties of Bounded Linear Operations

2.1 Bounded Linear Operations on Hilbert Space
2.2 Partial Isometry Operator and Polar Decomposition of an Operator
2.3 Polar Decomposition of an Operator and its Applications
2.4 Spectrum of an Operator
2.5 numerical Range of an Operator
2.6 Relations Among Several Classes of Non-normal Operators
2.7 Charactorizations of Convexoid Operators and Related Examples

3. Further Development of Bounded Linear Operators

3.1 Young Imequality and Holder-McCarthy Inequality
3.2 Lowner-Heinz Inequality and Furuta Inequality
3.3 Chaotic Order and the Relative Operator Entropy
3.4 Aluthge Transformation on P-Hyponormal Operators and Log-Hyponormal Operators
3.5 A Subclass of Paranormal Operators Including Loh-Hyponormal Operators and Several Related Classes
3.6 Operator Inequalities Associated With Kantorovich Inequality and Holder-McCarthy Inequality
3.7 Some Properties on Partial Isometry, Quasinormality and Paranormality
3.8 Weighted Mixed Schwarz Inequality and Generalized Schwarz Inequality
3.9 Selberg Inequality
3.10 An Extension of Heinz-Kato Inequality
3.11 Norm Inequalities Equivalent to Lower-Heinz Inequality
3.12 Norm Inequalities Equivalent to Heinz Inequality

Bibliography
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Taylor and Francis Books
Auteur(s)	Furuta Takayuki
Parution	19/02/2002
Nb. de pages	254
Format	15,5 x 23,3
Couverture	Broché
Poids	414g
Intérieur	Noir et Blanc
EAN13	9780415267991
ISBN13	978-0-415-26799-1