Seminar in operator theory and operator algebras
Fall 2007


The seminar is organized by Tom Kriete, and this webpage is maintained by David Sherman. We usually meet Tuesdays from 3:30 to 4:30 in Kerchof 205 (Tom Kriete's office).



September 4

Tom Kriete

Introduction to K-theory for C*-algebras

This series of talks, with various speakers, will continue for much of the year as the schedule permits. Lectures on other topics, both in-house and by visiting speakers, will be interspersed throughout.

September 11

David Sherman/Tom Kriete

Introduction to K-theory for C*-algebras

Notes from the first two seminars

September 18

Tom Kriete

Introduction to K-theory for C*-algebras

Notes

September 25

Katie Quertermous/Tom Kriete

Introduction to K-theory for C*-algebras

Notes

October 2

Tom Kriete

Introduction to K-theory for C*-algebras

Notes

October 9

No meeting (reading day)

October 16

Tom Kriete

Introduction to K-theory for C*-algebras

Notes

October 23

David Sherman

Why operator spaces? / Introduction to K-theory for C*-algebras

(first half) I'll introduce operator spaces and hopefully give some idea why they're interesting. This is intended to prep the audience for Zarikian's talk Nov. 13, and it may all be review for attendees of Tom's course last semester.
(second half) I'll introduce the dimension semigroup of a C*-algebra, then explain the Grothendieck construction which leads to K0.

Notes

October 30

Kerchof 326

Brent Carswell, Allegheny College

Conditional expectation, Bergman projection, and disintegration of Lebesgue area measure

Aleksandrov proved that on the space L2(T,m), where m denotes normalized Lebesgue measure on the unit circle T, the conditional expectation operator associated with a σ-algebra of Lebesgue measurable subsets of T commutes with the Riesz projection if and only if the σ-algebra is generated by an inner function. The conditional expectation operator associated with an inner function is closely linked to the Clark-Aleksandrov measure determined by the same inner function. In this talk, we examine the extent to which Aleksandrov's result translates to the setting of the unit disk, where T, m, and the Riesz projection are replaced by the disk, area measure, and the Bergman projection, respectively. For this, we introduce a certain family of measures, which can be viewed as the disk version of the Clark measures.

Notes

November 5 (Monday)

3:30 PM
Kerchof 205

Pietro Poggi-Corradini, Kansas State University (visiting George Mason University)

Some new versions of Schwarz's lemma using diameters, capacity and area

We first recall Schwarz's lemma and its generalization using diameter given by Landau and Toeplitz in 1907. We then give a new proof of this result which allows to use higher diameters and even capacity. Time permitting we will sketch what happens when using area and we will state some open problems. This is joint with Bob Burckel, Don Marshall, David Minda, and Tom Ransford.

Notes

November 13

Kerchof 326

Vrej Zarikian, U.S. Naval Academy

Operator spaces, multipliers, and applications

After a brief review of operator space theory we will discuss left multipliers of operator spaces, as introduced by Blecher. These are linear maps on the operator space which in some concrete representation of the operator space become left multiplication by a fixed operator. We then present a fundamental theorem of Blecher, Effros, and the speaker which characterizes left multipliers abstractly (i.e. without reference to a concrete representation of the operator space). As applications we give elegant proofs of the Blecher-Ruan-Sinclair characterization of unital (non-self-adjoint) operator algebras and a Banach-Stone theorem for such algebras. Time permitting, we indicate how one-sided multiplier theory leads to a one-sided M-ideal theory for operator spaces, analogous to the (two-sided) M-ideal theory of Banach spaces introduced by Alfsen and Effros in the 1970s.

Slides from the talk, including a proof

November 20

No meeting (Thanksgiving week)

November 30 (Friday)

David Blecher, University of Houston

canceled due to illness

December 4

David Sherman

Greatest hits of C*-algebraic K-theory

Next semester Tom Kriete and I plan to lead a working seminar on this topic, based on Rordam's book. In this talk I will try to give some idea of the main objects, the main theorems, and what can be done with them. I will snobbishly ignore details and may even lie a little. Like any short compilation, this will be woefully incomplete -- interested parties should buy the boxed set in the spring!



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