1st Edition
Invitation to Linear Operators From Matrices to Bounded Linear Operators on a Hilbert Space
By Takayuki Furuta
Copyright 2001
266 Pages
by
CRC Press
268 Pages
by
CRC Press
272 Pages
by
CRC Press
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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.
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
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
Biography
Takayuki Furuta
"[T]he book is quite comprehensive."
- Zentralblatt fur Mathematik, Vol. 1029
