Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space, 1st Edition (Paperback) book cover

Invitation to Linear Operators

From Matrices to Bounded Linear Operators on a Hilbert Space, 1st Edition

By Takayuki Furuta

CRC Press

266 pages

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Paperback: 9780415267991
pub: 2001-07-26
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Description

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.

Reviews

"[T]he book is quite comprehensive."

- Zentralblatt fur Mathematik, Vol. 1029

Table of Contents

HILBERT SPACES

Inner Product Spaces and Hilbert Spaces

Jordan-Neuman Theorem

Orthogonal Decomposition of Hilbert Space

Gram-Schmidt Orthonormal Procedure and its Applications

FUNDAMENTAL PROPERTIES OF BOUNDED LINEAR OPERATIONS

Bounded Linear Operations on Hilbert Space

Partial Isometry Operator and Polar Decomposition of an Operator

Polar Decomposition of an Operator and its Applications

Spectrum of an Operator

Numerical Range of an Operator

Relations Among Several Classes of Non-normal Operators

Characterizations of Convexoid Operators and Related Examples

FURTHER DEVELOPMENT OF BOUNDED LINEAR OPERATORS

Young Inequality and Holder-McCarthy Inequality

Lowner-Heinz Inequality and Furuta Inequality

Chaotic Order and the Relative Operator Entropy

Aluthge Transformation on P-Hyponormal Operators and Log-Hyponormal Operators

A Subclass of Paranormal Operators Including Loh-Hyponormal Operators and Several Related Classes

Operator Inequalities Associated With Kantorovich Inequality and Holder-McCarthy Inequality

Some Properties on Partial Isometry, Quasinormality and Paranormality

Weighted Mixed Schwarz Inequality and Generalized Schwarz Inequality

Selberg Inequality

An Extension of Heinz-Kato Inequality

Norm Inequalities Equivalent to Lower-Heinz Inequality

Norm Inequalities Equivalent to Heinz Inequality

Bibliography

Index

Subject Categories

BISAC Subject Codes/Headings:
MAT007000
MATHEMATICS / Differential Equations
MAT037000
MATHEMATICS / Functional Analysis