Polynomials on Banach spaces with unconditional bases

We study the classes of homogeneous polynomials on a Banach space with unconditional Schauder basis that have unconditionally convergent monomial expansions relative to this basis. We extend some results of Matos, and we show that the homogeneous polynomials with unconditionally convergent expansions coincide with the polynomials that are regular with respect to the Banach lattices structure of the domain.

Shared Education in contested spaces: How collaborative networks improve communities and schools

Societies which suffer from ethnic and political divisions are often characterised by patterns of social and institutional separation, and sometimes these divisions remain even after political conflict has ended. This has occurred in Northern Ireland where there is, and remains, a long-standing pattern of parallel institutions and services for the different communities. A socially significant example lies in the education system where a parallel system of Catholic and Protestant schools has been in place since the establishment of a national school system in the 1830s. During the years of political violence in Northern Ireland a variety of educational interventions were implemented to promote reconciliation, but most of them failed to create any systemic change. This paper describes a post-conflict educational initiative known as Shared Education which aims to promote social cohesion and school improvement by encouraging sustained and regular shared learning between students and broader collaboration between teachers and school leaders from different schools. The paper examines the background to work on Shared Education, describes a ‘sharing continuum’ which emerged as an evaluation and policy tool from this work and considers evidence from a case study of a Shared Education school partnership in a divided city in Northern Ireland. The paper will conclude by highlighting some of the significant social and policy impact of the Shared Education work.