Hilbert Space Operators: A Problem Solving Approach

ISBN-13: 9780817632427 / Angielski / Miękka / 2003 / 149 str.

Carlos S. Kubrusly

Opis

This is a problem book on Hilbert space operators (Le., on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre l: t only a part of the so-called single operator theory. Selected prob lems, ranging from standard textbook material to points on the boundary of the subject, are organized into twelve chapters. The book begins with elementary aspects of Invariant Subspaces for operators on Banach spaces 1. Basic properties of Hilbert Space Operators are introduced in in Chapter Chapter 2, Convergence and Stability are considered in Chapter 3, and Re ducing Subspaces is the theme of Chapter 4. Primary results about Shifts on Hilbert space comprise Chapter 5. These are introductory chapters where the majority of the problems consist of auxiliary results that prepare the ground for the next chapters. Chapter 6 deals with Decompositions for Hilbert space contractions, Chapter 7 focuses on Hyponormal Operators, and Chapter 8 is concerned with Spectral Properties of operators on Banach and Hilbert spaces. The next three chapters (as well as Chapter 6) carry their subjects from an introductory level to a more advanced one, including some recent results. Chapter 9 is about Paranormal Operators, Chapter 10 covers Proper Contractions, and Chapter 11 searches through Quasi reducible Operators. The final Chapter 12 commemorates three decades of The Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators."

Recenzje

"...the author treats many new subjects of operator theory for graduate students and mathematicians, i.e., quasihyponormal operators, paranormal operators, proper contractions, quasireducible operators, a detailed presentation of the Lomonosov theorem on nontrivial hyperinvariant subspaces for compact operators, etc. This book will be of benefit to graduate students (in mathematics, physics, engineering, economics, and statistics) and many mathematicians."

-Zentralblatt MATH

"...many totally new subjects are offered to the potential reader.... The author has great teaching experience reflected by the skillful selection of background material, the gradual statements of the problems, and the detailed presentation of the solutions. The book is intended [for] an audience mainly formed by various types of graduate students: in mathematics, statistics, physics and, perhaps, in engineering and economics. It can be useful even for working mathematicians, as a reference book in a broad sense...."

-Mathematical Reviews

Spis treści

Preface * Invariant Subspaces * Hilbert Space Operators * Convergence and Stability * Reducing Subspaces * Shifts * Decompositions * Orthogonality * Hyponormal Operators * Spectral Properties * Paranormal Operators * Proper Contractions * Quasireducible Operators * The Lomonosov Theorem * Bibliography * Index

O autorze

Carlos Kubrusly was born in Rio de Janeiro in November 1947. He received his Ph.D. from the University of Warwick in 1976, held postdoctoral visiting research positions at the Universities of Warwick and Bonn, and has been a faculty member of Catholic University of Rio de Janeiro since 1972, where he became a full professor in 1988. Professor Kubrusly has published over a hundred scientific articles in international journals and proceedings of international conferences. He has participated in about forty scientific conferences, all with paper presentation, including plenary sections at the Toulouse IFAC Symposium in 1982 and at the Newport Beach SOTA Conference in 1998, and has also been a member of program committees of several international conferences.