Monograph:

  • Noncommutative Dynamics and E-semigroups

  • Published in the series Springer Monographs in Mathematics....

    Download a sample chapter as a pdf file.

    R. Srinivasan has pointed out an error in the proof of Lemma 13.6.5 on page 408. It is not hard to repair; here is his fix.

    Textbooks:

  • A Short Course on Spectral Theory

  • An introduction to spectral theory and modern analysis, based on my lectures for the Berkeley course Mathematics 206.

    Chapter 1: Spectral Theory and Banach Algebras

    Chapter 2: Operators on Hilbert Space

    Chapter 3: Asymptotics: Compact Perturbations and Fredholm Theory

    Chapter 4: Methods and Applications

    Download a more detailed table of contents in either dvi format or pdf format.

    Springer Graduate Texts in Mathematics volume 209, published 6 November, 2001.

    I welcome feedback from the users of his text.
    Download the errata list in either dvi format or pdf format.

  • An Invitation to C*-algebras

  • Basic theory of C*-algebras, their representations, and multiplicity theory, including a self-contained chapter on analytic Borel structures.

    Springer Graduate Texts in Mathematics volume 39, reprinted 1998.

    Download the errata list in pdf format.

    Lectures in streaming video:


    In order to view these lectures properly, you need a fast (cable or DSL) internet connection.

  • Lecture 1: Interactions in noncommutative dynamics

  • Lecture 2: Curvature and Dirac operator in multivariable operator theory

    Research papers:


    The most recent papers are at the top of the list, with a link to the location of the preprint on the arXiv. The older papers are posted in dvi and/or pdf format. pdf files can be viewed or printed using Adobe's free Acrobat Reader. I am no longer posting the TeX source files. If (for some reason) you are interested in seeing the sources, send me an email.

    Detailed references to all my published papers, along with Math Reviews and related information, can be accessed by following the Bibserver link on my departmental page.

    As you move down the list, you will find papers that have already been published. Many of the titles of published papers carry a link to the pdf file produced by the journal where it appeared, denoted "journal.pdf". Clicking on that might get you an electronic reprint of the article, if your library is a subscriber.

  • Helson and subdiagonal operator algebras (Posted 21 January, 2011)
    arXiv
  • Dilation theory yesterday and today (Posted 28 February, 2009)
    arXiv
  • The noncommutative Choquet boundary III: Operator systems in matrix algebras (Posted 25 October, 2008)
    arXiv
  • The noncommutative Choquet boundary II: Hyperrigidity (Posted 15 October, 2008)
    arXiv
  • Maximal vectors in Hilbert space and quantum entanglement (Updated 4 May, 2008)
    arXiv
  • Quantum channels that preserve entanglement (Updated 4 May, 2008)
    arXiv
  • The probability of entanglement (Updated 4 May, 2008)
    arXiv
    journal.pdf
  • Lifting endomorphisms to automorphisms (with Dennis Courtney) (Posted 3 March, 2007)
    abstract
    pdf
  • The noncommutative Choquet boundary (Posted 11 January, 2007)
    abstract
    pdf
  • Asymptotic Lifts of Positive linear maps (with Erling Stormer) (Posted 14 November, 2006)
    abstract
    pdf
  • The Asymptotic Lift of a Completely Positive map (Updated 10 July, 2006)
    abstract
    pdf
  • Diagonals of normal operators with finite spectrum (Posted 15 June, 2006)
    abstract
    pdf
  • On the existence of E_0-semigroups (Posted 8 May, 2006)
    abstract
    pdf
  • Diagonals of trace-class operators (with Richard Kadison) (Updated 3 October, 2005)
    abstract
    pdf
  • Quotients of Standard Hilbert modules (Revised 5 November, 2005)
    abstract
    pdf
  • The free cover of a row contraction (Updated 27 April, 2004)
    abstract
    dvi
    pdf
    journal.pdf
  • p-summable commutators in dimension d (Posted 10 August, 2003)
    abstract
    dvi
    pdf
  • The Universal A-dynamical System (Posted 6 August, 2003)
    abstract
    dvi
    pdf
  • Asymptotic Stability I: Completely Positive Maps (Updated 11 June, 2003)
    abstract
    dvi
    pdf
  • Four Lectures on Noncommutative Dynamics (updated 1 April, 2003)
    abstract
    dvi
    pdf
  • Generators of Noncommutative Dynamics (posted 16 January, 2002)
    abstract
    dvi
    pdf
  • The structure of Spin Systems (Joint with Geoff Price: updated 9 April, 2003)
    abstract
    dvi
    journal.pdf
  • Infinite tensor products of completely positive semigroups (Joint with Geoff Price: posted 25 March, 2001)
    abstract
    dvi
    pdf
    j ournal.pdf
  • The Dirac operator of a commuting d-tuple (Updated 6 June, 2001)
    abstract
    dvi
    pdf
    journal.pdf
  • The domain algebra of a CP semigroup (Posted 24 May, 2000)
    abstract
    dvi
    pdf
    journal.pdf
  • The heat flow of the CCR algebra (Posted 12 March, 2000)
    abstract
    dvi
    pdf
  • Interactions in noncommutative dynamics (Updated 4 Feb, 2000)
    abstract
    dvi
    pdf
    j ournal.pdf
  • The curvature invariant of a Hilbert module over C[z_1,...,z_d] (Updated 26 Aug 99)
    abstract
    dvi
    pdf
    journal.pdf
    Published summary in PNAS (USA) pdf.
  • Subalgebras of C*-algebras III: multivariable operator theory (Revised 18 May 97)
    abstract
    dvi
    pdf
  • Pure E_0-semigroups and absorbing states
    abstract
    journal.pdf
  • The index of quantum dynamical semigroups
    abstract
    journal.pdf
  • On the index and dilations of completely positive semigroups
    abstract
    dvi
    pdf
  • Lecture notes and snippets

  • Lecture: Maximal vectors in Hilbert space and quantum entanglement (Updated 20 August, 2008)
    pdf
  • Notes on continuous tensor products (Posted 7 February, 2006)
    pdf
  • Several Problems in Operator Theory (Posted 18 June, 2003)
    abstract
    dvi
    pdf
  • Notes on the unique extension property (Posted 4 May, 2003)
    abstract
    dvi
    pdf
  • The Canonical Anticommutation Relations (Posted 25 May 2001)
    abstract
    dvi
    pdf
  • Does Quantum Field Theory Exist? (Posted 7 Feb 2000)
    abstract
    dvi
    pdf
  • Notes on measure and integration in locally compact spaces (Updated and corrected 2 Sept 99)
    abstract
    dvi
    pdf
  • Eigenvalue lists of noncommutative probability distributions (Posted 10 Sept. 1999)
    abstract
    dvi
    pdf
  • For E_0-semigroup zealots only (Posted 10 Sept. 1999)
    abstract
    dvi
    pdf
  • Some not-so-new papers

  • Minimal E_0-semigroups. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • Dynamical invariants for noncommutative flows. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • Path spaces, continuous tensor products, and E_0-semigroups. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • E_0-semigroups and quantum field theory. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • C*-algebras and Numerical linear algebra. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
    journal.pdf
  • C*-algebras and Numerical linear algebra II. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • The role of C*-algebras in infinite dimensional numerical linear algebra. (Updated 7 June, 2001)
    abstract
    dvi
    pdf
  • Discretized CCR algebras. (Posted 9 June, 2001)
    abstract
    dvi
    pdf
  • Non-commutative spheres and numerical quantum mechanics. (Updated 7 June, 2001)
    abstract
    dvi
    pdf