Seminar in operator theory and operator algebras (MATH 9310)
Spring 2015


The seminar is organized by David Sherman. We meet Tuesdays 4-5 in Kerchof 326. Due to regrettable inertia and the usual overload of January/February colloquia, the seminar kicks off in March.


March 3
Ker 317

Elias Katsoulis, East Carolina University

Operator algebras for multivariable C*-dynamics

I will present various algebras associated with multivariable dynamical systems over arbitrary C*-algebras. These algebras demonstrate a strong rigidity that allows them to encode well the dynamical system from which they originate. This is reflected in their classification theory, which I will discuss in detail. If time permits, I will also describe a promising direction for obtaining computable invariants through the use of local maps, e.g., local derivations.

March 17

Aon seimineár. Sláinte!

March 24

Bill Ross, University of Richmond

The range of a Toeplitz operator

In this joint work with Emmanuel Fricain and Andreas Hartmann, we explore the range of a co-analytic Toeplitz operator. In particular, we examine the boundary behavior of functions in the range as well as a natural orthogonal decomposition of the range with respect to the range norm.

March 31

David Sherman, UVa

Two new theorems about similar matrices

It is well-known that if A and B are self-adjoint complex matrices, AB and BA are similar. Is this still true if A and B are merely normal?

We say that a matrix V is a partial isometry if V*V is a projection; which matrices are similar to partial isometries?

Somewhat to my surprise, I have co-authored a paper with Stephan Garcia and Gary Weiss that answers these two questions. I'll present solutions, examples establishing sharpness of the results, and some open problems.

April 7

No seminar - Fields Medalist Vaughan Jones (Vanderbilt University) will give a three-lecture series April 6-8.

April 14

Kristin Courtney, UVa

Isometries of the Toeplitz matrix algebra

I will discuss some results from the titular paper by Farenick, Mastnak, and Popov, which was posted to arXiv in February of this year. The paper follows along a common theme in analysis/linear algebra of characterizing "preserver" maps on (subalgebras of) Mn(C). The two primary results of the paper are a characterization of continuous multiplicative isometries and a characterization of linear isometries on the Toeplitz subalgebra. I will present some background and a proof of the second result, namely: a linear isometry from the Toeplitz subalgebra of Mn(C) into Mn(C) is multiplication on the left and right by unitaries. The remaining time will be dedicated to corollaries and consequences.

Ken Davidson (University of Waterloo) will give the department colloquium on Thursday April 16 at 4 PM in Kerchof 317.

April 21

Scott Atkinson, UVa

A tubular characterization of hyperfiniteness, part 1 of 2

These talks will roughly follow the narrative of Kenley Jung's celebrated 2006 paper titled "Amenability, tubularity, and embeddings into Rω." The main result states that a (separable) von Neumann algebra is hyperfinite if and only if there is exactly one embedding into an ultrapower of the hyperfinite II1-factor R up to unitary conjugacy. In the first talk, we will introduce the relevant definitions (including 'tubular'--the mathematical notion, not the adjective used by Teenage Mutant Ninja Turtles) and then proceed with the proof of this characterization. In the second talk, we will complete the proof and discuss some of the consequences of this result in the literature and in my current research.

April 28

Scott Atkinson, UVa

A tubular characterization of hyperfiniteness, part 2 of 2

These talks will roughly follow the narrative of Kenley Jung's celebrated 2006 paper titled "Amenability, tubularity, and embeddings into Rω." The main result states that a (separable) von Neumann algebra is hyperfinite if and only if there is exactly one embedding into an ultrapower of the hyperfinite II1-factor R up to unitary conjugacy. In the first talk, we will introduce the relevant definitions (including 'tubular'--the mathematical notion, not the adjective used by Teenage Mutant Ninja Turtles) and then proceed with the proof of this characterization. In the second talk, we will complete the proof and discuss some of the consequences of this result in the literature and in my current research.





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