Seminar in operator theory and operator algebras (MATH 931)
Fall 2008

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

September 2


September 9

no meeting

September 16

Bill Ross, University of Richmond

An operator theory look at some classical extremal problems I

In this joint work with Stephan Garcia (Pomona College), I will relate some classical linear extremal problems on H1 to truncated Toeplitz operators and complex symmetric operators. Along the way, I will obtain some known results of Macintyre, Rogosinski, Khavinson, and Golusin but with operator theory - and not function theory - proofs.

September 23

Bill Ross, University of Richmond

An operator theory look at some classical extremal problems II

(See previous week's abstract.)

September 30

Tom Kriete, UVa

Invariant subspaces of parabolic composition operators

This is the first in a series of talks based on the paper Invariant subspaces of parabolic self-maps in the Hardy space by A. Montes-Rodriguez, M. Ponce-Escudero, and S. A. Shkarin.

October 7

Tom Kriete, UVa

Invariant subspaces of parabolic composition operators II

October 14


October 21

Tom Kriete, UVa

Invariant subspaces of parabolic composition operators III

October 28

Katherine Heller, UVa

Compactness of weighted composition operators between Sp spaces

Let φ and ψ be two analytic functions defined on the disc such that φ(D) ⊂ D. The operator given by f → ψ(f ° φ) is called a weighted composition operator. For each 1 ≤ p ≤ ∞, let Sp be the space of analytic functions on D whose derivatives belong to the Hardy space Hp. In this talk, we'll discuss compactness of weighted composition operators from Sp into Sq for 1 ≤ p,q ≤ ∞.

Reference: M. D. Contreras and A. G. Hernandez-Diaz, Weighted composition operators on spaces of functions with derivative in a Hardy space, JOT 52 (2004), 173--184.

November 4

David Sherman, UVa

What is a II1 factor?

Some answers to the title question: an infinite-dimensional analogue of a matrix algebra; a noncommutative version of a probability space; a completion of a group algebra.

November 11

Damon Hay, University of North Florida

Noncommutative peak phenomena

A peak set for a function algebra is a closed subset on which some function in the algebra is identically 1 and has modulus less than 1 off the set. Peak sets and peak interpolation arise in the structure of ideals, Choquet boundaries and in function algebra variants of Urysohn's lemma. We will survey recent work on noncommutative peak phenomena for operator algebras. In particular, we will discuss analogues of peak sets and peak interpolation for operator algebras and the related topics of one-sided ideals, proximinality, and other applications in operator algebras which are not necessarily self-adjoint.

November 18

Kevin Beanland, Virginia Commonwealth University

Weak Hilbert spaces

The notion of weak Hilbert Banach space was introduced by Gilles Pisier in the late 1980s. In this talk we discuss some results relating to these spaces and outline the construction of a weak Hilbert space not isomorphic to any of its proper subspaces.

November 25

no meeting (just before Thanksgiving break)

December 2

Alexis Alevras, U.S. Naval Academy

One-parameter flows of B(H)

E0-semigroups are one-parameter semigroups of endomorphisms of B(H). They can be thought of as quantized analogues of semigroups of isometries. E0-semigroups appear naturally in quantum field theory, in the study of open quantum systems, as well as in (non-commutative) probability theory. The central problem in the theory is classifcation up to a natural notion of equivalence called cocycle conjugacy.

The talk will contain an up to date general overview of the theory of E0-semigroups and the classifcation project.

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