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 |
ORGANIZATIONAL MEETING |
September 9 |
no meeting |
September 16 |
Bill Ross, University of RichmondAn operator theory look at some classical extremal problems IIn 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 RichmondAn operator theory look at some classical extremal problems II(See previous week's abstract.) |
September 30 |
Tom Kriete, UVaInvariant subspaces of parabolic composition operatorsThis 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, UVaInvariant subspaces of parabolic composition operators II |
October 14 |
READING DAY - HOLIDAY |
October 21 |
Tom Kriete, UVaInvariant subspaces of parabolic composition operators III |
October 28 |
Katherine Heller, UVaCompactness of weighted composition operators between Sp spacesLet 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, UVaWhat 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 FloridaNoncommutative peak phenomenaA 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 UniversityWeak Hilbert spacesThe 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 AcademyOne-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. |