PLACE: Milner 317

SPEAKER: Gilles Pisier, TAMU

TITLE: Remarks on B(H) \otimes B(H)

ABSTRACT: We will review the existing proofs that the min and max $C^*$-norms are different on $B(H) \otimes B(H)$ (originally due to Junge and the speaker) and present a shortcut that avoids any reference to the non separability of the set of finite dimensional operator spaces.

DATE: 4pm, Friday Sept. 17th

PLACE: Milner 317

SPEAKER: Razvan Anisca, TAMU

TITLE: Unconditional bases and decompositions in subspaces of $\ell_2(X)

ABSTRACT: If a Banach space $X$ is not isomorphic to a Hilbert space then $\ell_2(X)$ contains a subspace which has an unconditional finite dimensional decomposition (in short UFDD), but does not admit a UFDD with an uniform bound for the dimensions of the decomposition.

DATE: 4pm, Friday Sept. 24th

PLACE: Milner 317

SPEAKER: David Blecher, University of Houston

TITLE: Dual operator algebras: what they are

ABSTRACT: In joint work with Magajna, we have finally obtained the final form of the abstract characterization of weak*-closed algebras of Hilbert space operators. Operator spaces do turn out to be necessary, as we will show. We also mention connections to the theory of multipliers. This talk may be viewed as a sequel to Blecher's summer talk on the subject (although we will not assume any familiarity with that).

DATE: 4pm, Friday Oct. 1st

PLACE: Milner 317

SPEAKER: Gilles Pisier

TITLE: A characterization of nuclear C* algebras (including the proof)

ABSTRACT: A C* algebra is nuclear iff the cb norm of any bounded homomorphism is majorized by a multiple of the square of its norm.

DATE: 4pm, Friday Oct. 8th

PLACE: Milner 317

SPEAKER: Carl Pearcy, TAMU

TITLE: Hyperinvariant subspace lattices

ABSTRACT: Let (A) denote the set of all algebraic operators in L(H) (that is, the set of those T that satisfy a polynomial equation). The speaker and coauthors have shown recently that there exists a "very nice" fixed operator U in L(H) such that the hyperlattice Hlat(T) of every operator T in L(H)\(A) is to be found among the hyperlattices of the set of operators {U + K: K is compact and ||K|| is arbitrarily small}. Some of the ideas of the proof will be discussed.

DATE: 4pm, Friday Oct. 15th

PLACE: Milner 317

SPEAKER: No talk

TITLE:

ABSTRACT:

DATE: 4pm, Friday Oct. 22nd

PLACE: Milner 317

SPEAKER: Leonid Pastur, University of Paris

TITLE: Matrix models and orthogonal polynomials

ABSTRACT: click here. This is the third talk of his Frontiers series.

DATE: 4pm, Friday Oct. 29th

PLACE: Milner 317

SPEAKER: Xiang Fang, University of Alabama

TITLE: On the Fredholm index in several variables

ABSTRACT: I will describe how to define a joint Fredholm index for
two commuting operators. Two examples will be used as
motivations: the first is about the familar Hardy space, the second
is from a survey by M. Atiyah on K-theory.

To develop a theory for more operators, it is a surprising fact that
objects with a rich algebraic structure naturally enter the picture.
This leads to interplay between operator theory, complex
analysis, and commutative algebra. In particular, I will explain how
J.-P. Serre's classical work in local algebra is relavent to operator
theory.

DATE: 4pm, Friday Nov. 5th

PLACE: Milner 317

SPEAKER: Hsiang-Ping Huang, Univ. of Utah

TITLE: Irreducible hyperfinite II_{1} subfactors

ABSTRACT: In this talk, I will present a new technique to construct
irreducible hyperfinite II_{1} inclusions. The first example is a
series of inclusions of II_{1} factors inside the Pimnser-Popa
representation of Temperley-Lieb algebra R,
R \supset P_{1} \subset P_{2} \subset \cdots \supset
P_{n} \subset \cdot
with the property
R \cap P_{n}'= {\mathbb }, \cap_{n=1}^{\infty} P_{n}=
{\mathbb C}
[R: P_{1}] \geq \lambda, [P_{n}: P_{n+1}] \geq
\lambda

DATE: 4pm, Friday Nov. 12th NOTE:DUE TO THE DEPARTMENT RETREAT, THIS IS POSTPONED TO THE SPRING SEMESTER, DATE TBA

PLACE: Milner 317

SPEAKER: Ron Douglas, TAMU

TITLE: Some remarks on the Berger-Shaw Theorem and a conjecture of Arveson

ABSTRACT: In the seventies, Berger and Shaw showed that finitely cyclic hyponormal operators have trace-class self-commutators. Many people, including me, have thought about generalizations of this result to the several variables case and to the context of the Schatten p-class, but with little success. I have returned to the topic in connection with a conjecture of Arveson on the p-summability of the commutators of the restrictions to certain invariant subspaces of coordinate multipliers on the Bergman space over the ball and their adjoints. In my talk I will discuss this circle of ideas including some positive results and some approaches which don't seem to work. Finally, I will demonstrate some of the consequences that a positive solution to Arveson's conjecture would yield. In particular, one would obtain a new kind of index theorem in the K-homology for algebraic varieties.

DATE: 4pm, Friday Nov. 19th

PLACE: Milner 317

SPEAKER: Nirina Randrianarivony, TAMU

TITLE: $\ell_p$ ($p>2$) does not coarsely embed into a Hilbert space.

ABSTRACT: A coarse embedding of a metric space X into a metric space Y is a map f: X-->Y satisfying for every x, y in X:

\phi_1(d(x,y)) \leq d(f(x),f(y)) \leq \phi_2(d(x,y))

where \phi_1 and \phi_2 are nondecreasing functions on [0,\infty} with values in [0,\infty), with the condition that \phi_1(t) tends to \infty as t tends to \infty.

DATE: 4pm, Friday Dec. 3rd

PLACE: Milner 317

SPEAKER: Guoliang Yu, Vanderbilt University

TITLE:

ABSTRACT:

DATE: 4pm, Friday Feb 18th

PLACE: Milner 317

SPEAKER: Ron Douglas, TAMU

TITLE: Some remarks on the Berger-Shaw Theorem and a conjecture of Arveson

ABSTRACT: In the seventies, Berger and Shaw showed that finitely cyclic hyponormal operators have trace-class self-commutators. Many people, including me, have thought about generalizations of this result to the several variables case and to the context of the Schatten p-class, but with little success. I have returned to the topic in connection with a conjecture of Arveson on the p-summability of the commutators of the restrictions to certain invariant subspaces of coordinate multipliers on the Bergman space over the ball and their adjoints. In my talk I will discuss this circle of ideas including some positive results and some approaches which don't seem to work. Finally, I will demonstrate some of the consequences that a positive solution to Arveson's conjecture would yield. In particular, one would obtain a new kind of index theorem in the K-homology for algebraic varieties.

DATE: 4pm, Friday Feb 25th

PLACE: Milner 317

SPEAKER: Ken Dykema

TITLE: Twisted multiplicativity of the S-transform.

ABSTRACT: In the late '80s, Voiculescu invented the S-transform S_x of a (noncommutative) random variable x. It is an analytic function defined in terms of the moments of x. The relevant property is multiplicativity under freeness. Thus, for free random variables x and y, we have S_{xy}=S_x S_y. The S-transform can be used to compute the moment generating series of xy in terms of those for x and y. Voiculescu defined the S-transform and proved multiplicativity for scalar-valued random variables. In this talk, we consider B-valued random variables, where B is a Banach algebra. We broaden Voiculescu's definition and prove a twisted multiplicativity property that reduces to multiplicativity when B is commutative. Our proof relies on certain creation and annihilation operators on a Banach space analogue of full Fock space.

DATE: 4pm, Friday Mar 4th

PLACE: Milner 317

SPEAKER: Thomas Schlumprecht

TITLE: A reflexive Banach which is universal for uniform convex spaces

ABSTRACT: In 1980 J.Bourgain proved that a Banach space which contains (isomorphically) all reflexive separable Banach spaces must contain C[0,1] and, thus, all separable spaces and he asked whether or not there exists a reflexive space which contains all uniform convex spaces. We will give an affirmative answer to this question.

DATE: 4pm, Thursday Mar 10th (NOTE UNUSUAL DAY)

PLACE: Milner 317

SPEAKER: Christian Rosendal, Stanford Univ.

TITLE: Incomparable and minimal Banach spaces

ABSTRACT: Banach space theory underwent an explosive development a decade ago with discoveries of new exotic spaces using methods of W.T. Gowers and B. Maurey and solutions to many of the classical problems by several people. However, this also lead to new problems and hope for a better understanding of the isomorphism classes of subspaces of any given Banach space. We prove a dichotomy for Banach spaces saying that any infinite-dimensional Banach space contains either a minimal subspace or a continuum of incomparable subspaces. The proof relies heavily on the Ramsey type methods invented by W.T. Gowers and the solution of the distortion problem by E. odell and T. Schlumprecht, but also introduces new methods from logic.

DATE: 4pm, Friday Mar 18th

PLACE: Milner 317

SPEAKER: Spring Break, no talk.

TITLE:

ABSTRACT:

DATE: 4pm, Monday Mar 21st (NOTE UNUSUAL DAY)

PLACE: Milner 317

SPEAKER: Rongwei Yang, SUNY Albany

TITLE: Two variable operator theory in the Hardy space

ABSTRACT: Study of the unilateral shift operator in the classical Hardy space is a foundation for many important developments in operator theory and operator algebra. A two variable analogue of this study is believably to have far-reaching impacts on multivariable operator. This talk surveys some recent efforts along this line.

DATE: 4pm, Monday Mar 28th (NOTE UNUSUAL DAY)

PLACE: Milner 317

SPEAKER: Mihai Putinar, U.C. Santa Barbara

TITLE: Complex symmetric operators and applications

ABSTRACT: Complex symmetric matrices are less studied and used than hermitian symmetric matrices. I will trace back to Takagi, Schur, Siegel and Glazman the main contributions towards the classification theory of complex symmetric matrices. A novel polar factorization simplifies concaptually the classical works and opens a few possibilities for rather unexpected applications. I will show how this framework explains the completeness of the system of Fredholm eigenfunctions of a (planar) domain and how one can obtain the best norm estimates for certain non-selfadjoint boundary problems appearing in solid state physics.

Based on joint work with S. Garcia, E. Prodan and J. Danciger.

DATE: 4pm, Friday Apr 8th

PLACE: Milner 317

SPEAKER: Roger Smith

TITLE: Constructing the trace in the basic construction

ABSTRACT: Jones's theory of subfactors has the following ingredients: a finite index inclusion $B \subseteq N$ of finite factors, a projection $e_B$ of $L^2(N)$ onto $L^2(B)$ and another finite factor $<N,e_B>$ generated by $N$ and $e_B$, called the basic construction. Up to scalar multiples, this latter factor has a unique trace, so it is fortuitous that this trace has some nice extra properties. One would like this theory to generalize to an inclusion where $N$ is just a finite algebra with a faithful normal trace, because $<N,e_B>$ is a good algebra in which to carry out certain calculations about the pair $N, B$. It seems to have been assumed in the literature that this is a routine extension of the easy subfactor case, but I think that this is not so. In this talk I will show how to construct an appropriate trace on $<N,e_B>$.

DATE: 4pm, Friday Apr 15th

PLACE: Milner 317

SPEAKER: No seminar

TITLE:

ABSTRACT:

DATE: 4pm, Friday Apr 22nd

PLACE: Milner 317

SPEAKER: Laszlo Kerchy (Bolyai Institute and TAMU)

TITLE: Compressions of stable contractions

ABSTRACT: An operator is called stable if its powers converge to zero in the
strong operator topology.
The stability of compressions of stable contractions is discussed and a
sufficient orbit condition is given.
On the other hand, it is shown that there are non-stable compressions of
the 1-dimensional backward shift
and a complete characterization of weighted unilateral shifts with this
property is provided.
Dilations of bilateral weighted shifts to backward shifts are also
considered.

(Joint work with Vladimir Muller)

DATE: 4pm, Friday Apr 29th

PLACE: Milner 317

SPEAKER: Sandra Pott, Univ. of Glasgow

TITLE: John-Nirenberg type inequalities and a scale of dyadic rectangular BMO spaces on the bidisk

ABSTRACT: The dual space of the Hardy space $H^1(\mathbb{T}^2)$ on the bitorus has attracted much attention in recent years with the work of S.Ferguson, M. Lacey, C. Sadosky and others on the so-called "weak factorization problem " of $H^1(\mathbb{T}^2)$, which was solved in the positive by Ferguson and Lacey in 2002. Fefferman's celebrated duality theorem states that the dual of the Hardy space $H^1(\mathbb{T})$ is the space $BMOA(\mathbb{T})$, consisting of analytic functions on $\mathbb{T}$ satisfying the averaging condition \begin{equation} \label{bmo} \sup_{I \subseteq \mathbb{T}, I \text{ interval }} \left(\frac{1}{|I|} \int_I | b(t) - m_I b |^2 dt \right)^{1/2}< \infty, \end{equation} where $m_I b $ denotes the average of $b$ over $I$. By the John-Nirenberg Theorem, this supremum is equivalent to \begin{equation} \label{johnnir} \sup_{I \subseteq \mathbb{T}, I \text{ interval }} \left(\frac{1}{|I|} \int_I | b(t) - m_I b |^p dt \right)^{1/p} < \infty, \end{equation} for any $1 \le p < \infty$.

The Fefferman Duality Theorem theorem does not generalize in an obvious way to the multivariable setting. It is well-known that the averaging condition over rectangles corresponding to (\ref{bmo}) does not characterize the dual of $H^1(\mathbb{T}^2)$.

In this talk, we want to give a characterization of dyadic version of this dual by means of John-Nirenberg type properties over rectangles. That means, we find that if a certain "rectangular" version of (\ref{johnnir}) holds for all $1 \le p < \infty$, then $b$ is in the dual of $H^1(\mathbb{T}^2)$.

(This is joint work with Oscar Blasco (Valencia).)