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.
By:
Takayuki Furuta Imprint: CRC Press Country of Publication: United Kingdom Dimensions:
Height: 229mm,
Width: 152mm,
Spine: 33mm
Weight: 521g ISBN:9780415267991 ISBN 10: 0415267994 Pages: 266 Publication Date:26 July 2001 Audience:
Professional and scholarly
,
Professional and scholarly
,
Professional & Vocational
,
Undergraduate
,
Further / Higher Education
Format:Paperback Publisher's Status: Active
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. Charactorizations of Convexoid Operators and Related Examples. FURTHER DEVELOPMENT OF BOUNDED LINEAR OPERATORS: Young Imequality 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.
Takayuki Furuta
Reviews for Invitation to Linear Operators: From Matrices to Bounded Linear Operators on a Hilbert Space
"""[T]he book is quite comprehensive."" - Zentralblatt fur Mathematik, Vol. 1029"
