Hilbert Space Operators

1. Front Matter

   Pages i-xv

   PDF

2. Invariant Subspaces

   • Carlos S. Kubrusly

   Pages 1-11

3. Hilbert Space Operators

   • Carlos S. Kubrusly

   Pages 13-22

4. Convergence and Stability

   • Carlos S. Kubrusly

   Pages 23-32

5. Reducing Subspaces

   • Carlos S. Kubrusly

   Pages 33-40

6. Shifts

   • Carlos S. Kubrusly

   Pages 41-50

7. Decompositions

   • Carlos S. Kubrusly

   Pages 51-64

8. Hyponormal Operators

   • Carlos S. Kubrusly

   Pages 65-74

9. Spectral Properties

   • Carlos S. Kubrusly

   Pages 75-92

10. Paranormal Operators

    • Carlos S. Kubrusly

    Pages 93-108

11. Proper Contractions

    • Carlos S. Kubrusly

    Pages 109-116

12. Quasireducible Operators

    • Carlos S. Kubrusly

    Pages 117-128

13. The Lomonosov Theorem

    • Carlos S. Kubrusly

    Pages 129-142

14. Back Matter

    Pages 143-151

    PDF

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.

• Applied Mathematics
• Finite
• Hilbert space
• Invariant
• Operator theory
• Problem-solving
• algebra
• equation
• function
• functional analysis
• ksa
• mathematics
• proof
• theorem

"…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

• Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

  Carlos S. Kubrusly

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