Seminar in Operator Theory and Operator Algebras - Spring 2011, University of Virginia

Seminar in operator theory and operator algebras (MATH 9310)
Spring 2011

The seminar is organized by David Sherman. We meet Tuesdays 3:30-4:30 in Kerchof 326.

February 8	Tom Kriete, UVa A recent theorem of Cowen and Gallardo-Gutierrez: Almost unitary equivalence between certain composition and Toeplitz operators
February 15	no meeting
February 22	David Sherman, UVa Conditional expectations onto maximal abelian -subalgebras Consider a pure state on a maximal abelian -subalgebra (MASA) of B(l²): does it have a unique state extension to all of B(l²)? Dirac's 1949 text on quantum mechanics seems to assume that it does. However, in 1959 Kadison and Singer used a detailed calculation in Fourier analysis to prove that there are multiple conditional expectations (CEs) from B(l²) onto a continuous MASA; this implies that some pure states on the MASA have nonunique extensions to B(l²). They also showed that there is a unique CE from B(l²) onto a discrete MASA, famously leaving open the question of uniqueness of pure state extensions in this case. Chuck Akemann and I recently answered the general question, "When is there a unique CE from a semifinite von Neumann algebra onto a singly-generated MASA?" Our methods rely on the new observation that a unique CE onto a singly-generated MASA must be weak* continuous, and in particular provide a short, Fourier-free route to the results for B(l²). In this talk I'll focus on B(l²) and define all the basic terms.
March 1	Craig Kleski, UVa Commutative and noncommutative Choquet boundaries Let M be a linear subspace of C(X). The Choquet boundary of M encodes information about M, and can be used to recover the Shilov boundary of M. It is also closely related to peak points for M. We'll discuss examples in the commutative case, then generalize to separable C*-algebras. Time permitting, we'll also talk about recent work of Arveson that resolved an old open question about the noncommutative Choquet boundary.
March 8	Spring break
March 15	no meeting SEAM (and John Conway Day) will be held March 17-19 at the University of Florida.
March 22	no meeting
March 29	no meeting The colloquium on March 31 will be given by David Kerr, Texas A&M.
April 5	no meeting The colloquium on April 4 will be given by John McCarthy, Washington University in St. Louis.
April 12	no meeting
April 19	Paul Bourdon, Washington and Lee University Hardy spaces hospitable to Hermitian weighted composition operators
April 26	Bill Ross, University of Richmond Models for symmetric operators I
April 29 note special day 2:30 PM Ker 326	Vladimir Bolotnikov, The College of William and Mary Boundary interpolation problems for analytic self-maps of the unit disk We will present a solvability criterion for the following boundary interpolation problem: given a finite number of points on the unit circle, find an analytic self-map of the unit disk which has specified values as well as specified derivatives up to specified orders at these points. The values and derivatives are taken in the sense of non-tangential limits, and the order of the highest desired derivative can depend on the input point on the circle. Some partial results concerning the case of specifying an infinite number of derivatives will also be discussed.
May 2 note special day 3 PM Ker 128	Don Hadwin, University of New Hampshire When is an operator S an analytic function of an operator T? Here is the abstract.
May 3	Bill Ross, University of Richmond Models for symmetric operators II
May 5 note special day 1:15 PM Ker 128	GPOTS teaser Craig Kleski and David Sherman will preview their GPOTS talks.

You can reminisce about previous semesters at the links below:
Fall 2010 Spring 2010 Fall 2009 Spring 2009 Fall 2008 Spring 2008 Fall 2007 Spring 2007 Fall 2006 Spring 2006 Fall 2005 Spring 2005 Fall 2004 Spring 2004 Fall 2003 Spring 2003 Fall 2002