Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space

ISBN-13: 9780415267991 / Angielski / Miękka / 2001 / 266 str.

Takayuki Furuta; Furuta Furuta

Opis

Linear operator theory is a natural extension of matrix theory. This guide to linear operators explains, in easy to follow steps, the newest essential and fundamental results on linear operators based on matrix theory.

Recenzje

"[T]he book is quite comprehensive."
- Zentralblatt fur Mathematik, Vol. 1029

Spis treści

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

O autorze

Takayuki Furuta