© 2010

A Glimpse at Hilbert Space Operators

Paul R. Halmos in Memoriam

  • Sheldon Axler
  • Peter Rosenthal
  • Donald Sarason

Part of the Operator Theory Advances and Applications book series (OT, volume 207)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Paul Halmos

    1. Front Matter
      Pages 1-2
    2. John Ewing
      Pages 11-25
    3. Heydar Radjavi, Peter Rosenthal
      Pages 27-29
    4. Sheldon Axler, Peter Rosenthal, Donald Sarason
      Pages 33-40
    5. Sheldon Axler, Peter Rosenthal, Donald Sarason
      Pages 41-77
  3. Articles

    1. Front Matter
      Pages 79-79
    2. William Arveson
      Pages 99-123
    3. Sheldon Axler
      Pages 125-133
    4. Hari Bercovici
      Pages 135-176
    5. John B. Conway, Nathan S. Feldman
      Pages 177-194
    6. Raúl Curto, Mihai Putinar
      Pages 195-207
    7. Kenneth R. Davidson
      Pages 209-222
    8. Michael A. Dritschel, James Rovnyak
      Pages 223-254
    9. Paul S. Muhly
      Pages 255-285
    10. Gilles Pisier
      Pages 325-339

About this book


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

Editors and affiliations

  • Sheldon Axler
    • 1
  • Peter Rosenthal
    • 2
  • Donald Sarason
    • 3
  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada
  3. 3.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

Bibliographic information

  • Book Title A Glimpse at Hilbert Space Operators
  • Book Subtitle Paul R. Halmos in Memoriam
  • Editors Sheldon Axler
    Peter Rosenthal
    Donald Sarason
  • Series Title Operator Theory Advances and Applications
  • DOI
  • Copyright Information Birkhäuser Basel 2010
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0346-0346-1
  • Softcover ISBN 978-3-0348-0310-6
  • eBook ISBN 978-3-0346-0347-8
  • Edition Number 1
  • Number of Pages X, 362
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operator Theory
  • Buy this book on publisher's site


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)