The Great Stone of Fourstones, a glacial deposit on the moorlands of Tatham Fells straddling the county border between North Yorkshire and Lancashire, near Bentham in the District of Craven.

Image

Plan

Click here to join in
via MS Teams




all times British Summer Time

10-10.15am: Welcome,

10.15-10.45: Jared White,

10.50-11.20: Niels Laustsen,

11.25-11.55: Matt Daws.

Titles and abstracts

This special event

is dedicated to celebrating the contributions to mathematical analysis of Garth Dales on the occasion of his retirement.

Garth Dales

Confirmed speakers

Matthew Daws (UCLan, Preston)

Jared White (Lancaster and Open University)

Niels J. Laustsen (Lancaster)

Talks

Matthew Daws

Title: Ring-theoretical infiniteness and ultrapowers

Abstract: For any ring, in particular, for a Banach algebra, there are notions of being "infinite", stated in terms of idempotents and equivalence. We investigate when such notions are preserved by the ultrapower (or ultraproduct) construction for Banach algebras. It turns out that having (or not) certain forms of norm control are central to answering this question, and we show by various examples that operator algebras and general Banach algebras can behave very differently. This is joint work with Bence Horvath.


Jared White

Title: Invariant means and Arens products

Abstract: Given a Banach algebra A its second dual A** is a Banach algebra with the so-called Arens product. Let G be an amenable group. We introduce a subalgebra Asn(G) of 1(G)**, which is related to invariant means on the subnormal subgroups of G. We explain how the nilpotence of Asn(G) reflects the subnormal structure of G in the case that G is a just infinite group. Finally we discuss how this sheds some light on the nilpotence of rad 1(G)**.


Niels J. Laustsen

Title: A C(K)-space with few operators

Abstract: I shall report on joint work with Piotr Koszmider (IMPAN, Warsaw), published earlier this year in Advances in Mathematics, concerning the closed subspace of generated by c0 and the characteristic functions of elements of an uncountable, almost disjoint family A of infinite subsets of the natural numbers. This Banach space has the form C0(KA) for a locally compact Hausdorff space KA that is known under many names, including Ψ-space and Isbell-Mrówka space.

Koszmider and I construct an uncountable, almost disjoint family A such that the algebra of all bounded operators on C0(KA) is as small as possible in the precise sense that every bounded operator on C0(KA) is the sum of a scalar multiple of the identity and an operator that factors through c0 (which in this case is equivalent to having separable range). This construction improves a previous construction of Koszmider, which required the assumption of the Continuum Hypothesis.

Contact Us

Please contact the organisers with any questions you may have:

Kevin Beanland,
Tomasz Kania
Niels Jakob Laustsen.