A Glimpse at Hilbert Space Operators

1. Front Matter

   Pages i-viii

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2. Paul Halmos

   1. Front Matter

      Pages 1-2

      PDF

   2. Paul Halmos — Expositor Par Excellence

      • V. S. Sunder

      Pages 3-10

   3. Paul Halmos: In His Own Words

      • John Ewing

      Pages 11-25

   4. Obituary: Paul Halmos, 1916–2006

      • Heydar Radjavi, Peter Rosenthal

      Pages 27-29

   5. Mathematical Review of “How to Write Mathematics” by P.R. Halrnos

      • G. Piranian

      Pages 31-31

   6. Publications of Paul R. Halmos

      • Sheldon Axler, Peter Rosenthal, Donald Sarason

      Pages 33-40

   7. Photos

      • Sheldon Axler, Peter Rosenthal, Donald Sarason

      Pages 41-77

3. Articles

   1. Front Matter

      Pages 79-79

      PDF

   2. What Can Hilbert Spaces Tell Us About Bounded Functions in the Bidisk?

      • Jim Agler, John E. McCarthy

      Pages 81-97

   3. Dilation Theory Yesterday and Today

      • William Arveson

      Pages 99-123

   4. Toeplitz Operators

      • Sheldon Axler

      Pages 125-133

   5. Dual Algebras and Invariant Subspaces

      • Hari Bercovici

      Pages 135-176

   6. The State of Subnormal Operators

      • John B. Conway, Nathan S. Feldman

      Pages 177-194

   7. Polynomially Hyponormal Operators

      • Raúl Curto, Mihai Putinar

      Pages 195-207

   8. Essentially Normal Operators

      • Kenneth R. Davidson

      Pages 209-222

   9. The Operator Fejér-Riesz Theorem

      • Michael A. Dritschel, James Rovnyak

      Pages 223-254

   10. A Halmos Doctrine and Shifts on Hilbert Space

       • Paul S. Muhly

       Pages 255-285

   11. The Behavior of Functions of Operators Under Perturbations

       • V. V. Peller

       Pages 287-324

   12. The Halmos Similarity Problem

       • Gilles Pisier

       Pages 325-339

Paul Richard Halmos, who lived a life of unbounded devotion to mathematics and to the mathematical community, died at the age of 90 on October 2, 2006. This volume is a memorial to Paul by operator theorists he inspired. Paul’sinitial research,beginning with his 1938Ph.D. thesis at the University of Illinois under Joseph Doob, was in probability, ergodic theory, and measure theory. A shift occurred in the 1950s when Paul’s interest in foundations led him to invent a subject he termed algebraic logic, resulting in a succession of papers on that subject appearing between 1954 and 1961, and the book Algebraic Logic, published in 1962. Paul’s ?rst two papers in pure operator theory appeared in 1950. After 1960 Paul’s research focused on Hilbert space operators, a subject he viewed as enc- passing ?nite-dimensional linear algebra. Beyond his research, Paul contributed to mathematics and to its community in manifold ways: as a renowned expositor, as an innovative teacher, as a tireless editor, and through unstinting service to the American Mathematical Society and to the Mathematical Association of America. Much of Paul’s in?uence ?owed at a personal level. Paul had a genuine, uncalculating interest in people; he developed an enormous number of friendships over the years, both with mathematicians and with nonmathematicians. Many of his mathematical friends, including the editors ofthisvolume,whileabsorbingabundantquantitiesofmathematicsatPaul’sknee, learned from his advice and his example what it means to be a mathematician.

• Functional analysis
• Hilbert space
• Mathematica
• Paul R. Halmos
• Volume
• behavior
• functions
• mathematics
• measure
• operator theory
• perturbation
• perturbation theory
• service
• similarity
• theorem

From the reviews:

“This is a book about the legacy of Paul Halmos in Operator Theory … . if you want to delve deeper into the research topic that was central to his career, this book is an excellent place to start. Any researcher starting out in Operator Theory, Operator Algebras or a related area would also be well-advised to read this volume. It gives an excellent portrayal the sweep of history in a mathematical discipline and how it can be affected by one man.” (Gordon MacDonald, The Mathematical Association of America, October, 2010)

• Department of Mathematics, San Francisco State University, San Francisco, USA

  Sheldon Axler

• Department of Mathematics, University of Toronto, Toronto, Canada

  Peter Rosenthal

• Department of Mathematics, University of California, Berkeley, USA

  Donald Sarason

Policies and ethics