# Analysis Seminar 2010-11

Tuesday September 28th, 2010 4.00pm UCD R. Smith Strictly convex norms, Maths Sem strange spaces and extra axioms, I There will also be an organisational meeting for the term's seminars. Tuesday October 5th 2.30pm TCD D. Bohle (Münster) Universal TROs 2.6 4.00 TCD W. Werner (Münster) JB*-triples and 2.6 differential geometry Tuesday October 12th 3.00pm UCD S. Dineen A monomial basis for Maths Sem the space of holomorphic functions 4.15 UCD R. Smith Strictly convex norms, Maths Sem strange spaces and extra axioms, II Tuesday October 19th 3.00pm UCD I. Netuka (Prague) Jensen measures and po- Maths Sem tential theory 4.15 UCD R. Harte Invariant subspaces and Maths Sem other animals Tuesday October 26th 2.30pm TCD M. Mackey Local derivations on Jor- 2.6 dan triples 4.00 TCD M. Ghergu Entire solutions for 2.6 semilinear elliptic PDEs Tuesday November 2nd 2.30pm TCD N. Tsirivas An extension of a theo- 2.6 rem of Seleznev 4.00 TCD P. Spain (Glasgow) How many hermitians 2.6 make a Hilbert space? Tuesday November 9th 3.00pm UCD B. Sehba A generalized weak fac- Maths Sem torization of Hp(Bn) with 0 < p < 1 4.15 UCD H. Render Polyharmonic functions Maths Sem of infinite order Tuesday November 16th 2.30pm TCD D. Kitson Upper continuity and 2.6 joint spectra 4.00 TCD R. Timoney Algebras satisfying the 2.6 von Neumann inequality Tuesday November 23rd 3.00pm UCD S. Gardiner Existence of universal Maths Sem Taylor series I 4.15 UCD V. Liskevich (Swansea) Some qualitative Maths Sem properties of second order elliptic and parabolic equations with lower order terms Tuesday November 30th 2.30pm TCD S. Gardiner Existence of universal 2.6 Taylor series II 4.00 TCD A. Bonami (Orleans) Two questions on Bloch 2.6 classes in bounded symmetric domains Tuesday December 7th 3.00pm UCD C. Boyd M-ideals and the bidual- Maths Sem ity problem for weighted spaces of holomorphic functions 4.15 UCD A. Brown Banach-Stone type Maths Sem theorems for spaces of polynomials

**Tuesday January 25th, 2011**4.00pm (place: UCD Maths Sem)

*Speaker:* R. Smith

*Title:* Killing Gruenhage spaces in ZFC

**Abstract: **
A topological space $X$ of cardinality at most the continuum is
called Gruenhage if there is a countable sequence of open subsets
$(U_n)$, such that given distinct $x, y \in X$, there exists $n$
such that either $x$ or $y$ is in $U_n$, but not both.

A space $X$ has a $G_\delta$-diagonal if its diagonal is a $G_\delta$ set in $X^2$ with the usual product topology.

Both notions concern the separation of distinct points in a controlled way, without using `too many' open sets. The classes of Gruenhage spaces and spaces having $G_\delta$-diagonals contain all metric spaces, together with some much wilder objects. Recently, the two classes have been shown to be relevant to Banach space geometry, but the relationship between them has been unclear.

In this talk, we present an example of a locally compact, Hausdorff, non-Gruenhage space having a $G_\delta$-diagonal. It improves upon a previous example of the speaker's, which relied on the continuum hypothesis.

There will also be an organisational meeting for the term's seminars.

** Tuesday February 1st**
4.00pm
(place: UCD
Maths Sem)

*Speaker:* M. Ghergu

*Title:* Elliptic inequalities in divergence form

** Tuesday February 8**
2.30pm
(place: TCD
2.6)

*Speaker:* R. Timoney

*Title:*A brief survey on hypercyclicity

** Tuesday February 8**
4.00
(place: TCD
2.6)

*Speaker:* H. Render

*Title:* Entire solutions of the Dirichlet problem for the strip for entire data

** Tuesday February 15**
3.00pm
(place: UCD
Maths Sem)

*Speaker:* M. Daws (Leeds)

*Title:* Shift invariant preduals of $\ell^1$

**Abstract: **
(Joint work with Richard Haydon, Thomas Schlumprecht and Stuart
White)

The Banach space $\ell^1$ has many different preduals-- for example, if $K$ is a locally compact, Hausdorff space which is countable, then the dual of $C_0(K)$ is $\ell^1(K)$, which is isomorphic to $\ell^1$ through picking an enumeration of $K$. There are also more "exotic" preduals-- the recent solution to the Scalar-Compact problem, by Argyros and Haydon, is a Banach space with is an $\ell^1$ predual.

In this talk, I will take as my indexing set the integers, and so we have the bilateral shift operator. We shall investigate if there exist preduals of $\ell^1$ with the additional property of making the bilateral shift weak*-continuous. For example, if a predual of the form $C_0(K)$ does this, then K must carry the discrete topology, so really we just get the canonical predual $c_0$. However, we give an explicit construction of a different predual which does make the bilaterial shift weak*-continuous.

Time allowing, I will show how Banach algebraic tools become useful (indeed, my original motivation came from Banach algebra theory). Indeed, some sort of classification is possible, and a more abstract construction leads to a wealth of examples.

** Tuesday February 15**
4.15
(place: UCD
Maths Sem)

*Speaker:* S. Gardiner

*Title:* Two phase quadrature domains I

** Tuesday February 22**
2.30pm
(place: TCD
2.6)

*Speaker:* S. Gardiner

*Title:* Two phase quadrature domains II

** Tuesday February 22**
4.00
(place: TCD
2.6)

*Speaker:* S. Buckley (NUIM)

*Title:* Rough $\mathrm{CAT}(0)$ spaces

** Tuesday March 1**
3.00pm
(place: UCD
Maths Sem)

*Speaker:* C. Boyd

*Title:* Extensions of completely bounded polynomials

** Tuesday March 1**
4.15
(place: UCD
Maths Sem)

*Speaker:* G. Costakis (U. Crete)

*Title:* Frequently recurrent operators

** Tuesday March 22**
2.30pm
(place: TCD
2.6)

*Speaker:* J. Kauppi (QUB)

*Title:* On dense ideals of C*-algebras and generalizations
of the Gelfand-Naimark Theorem

** Tuesday March 22**
4.00
(place: TCD
2.6)

*Speaker:* R. Harte

*Title:* Spectral permanence for the Moore-Penrose inverse

** Tuesday March 29**
3.00pm
(place: UCD
Maths Sem)

*Speaker:* A. Brown

*Title:* Banach-Stone type theorems on spaces of complex polynomials

** Tuesday March 29**
4.15
(place: UCD
Maths Sem)

*Speaker:* R. Levene

*Title:* Schur multipliers on von Neumann algebras

** Tuesday April 5**
4.00pm
(place: TCD
2.6)

*Speaker:* V. Burcea

*Title:* A normal form for a submanifold
$M\subset\mathbb{C}^{N+1}$
of codimension 2 near a flat CR singularity

** Tuesday April 12**
3.00pm
(place: UCD
Maths Sem)

*Speaker:* P. Hoffmann

*Title:* $(m,\infty)$-isometric operators

** Tuesday April 12**
4.15
(place: UCD
Maths Sem)

*Speaker:* J. Pres

*Title:* Champagne subregions of the unit disk

** Tuesday April 19**
2.30pm
(place: TCD
2.6)

*Speaker:* R. Gohm (Aberystwyth)

*Title:* Multi-variable operator theory and noncommutative probability

**Abstract: **We suggest some promising connections between these
fields and
illustrate
our point by discussing in some detail the recently introduced
transfer
functions for noncommutative Markov chains which are in fact
multi-analytic
operators in the sense of G. Popescu.

** Tuesday April 19**
4.00
(place: TCD
2.6)

*Speaker:* M. Mathieu (QUB)

*Title:* C*-Algebras of local multipliers

** Tuesday April 26th**
4.00pm
(place: UCD
Maths Sem)

*Speaker:* L. Moraes (Rio de Janiero)

*Title:* Lorch analytic functions