# 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