INVARIANT SUBSPACES AND HYPER-REFLEXIVITY FOR FREE SEMIGROUP ALGEBRAS

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very strong, but it has been established in only a very few cases. Moreover the prototypes of this class of algebras are the natural candidate for a non-commutative analytic Toeplitz algebra on n variables. The case we make for this analogy is very compelling. In particular, in this paper, the key to the invariant subspace analysis is a good analogue of the Beurling theorem for invariant subspaces of the unilateral shift. This leads to a notion of inner-outer factorization in these algebras. In a sequel to this paper [13], we add to this evidence by showing that there is a natural homomorphism of the automorphism group onto the group of conformal automorphisms of the ball in Cn

The voluntary and community sector in Blyth Valley - developing a vision for the future

1. Sustainable Cities Research Institute has produced this report following research carried out on behalf of Blyth Valley Local Strategic Partnership. The research involved documentary analysis, case studies, and interviews and focus groups involving key players within the Voluntary and Community Sector (VCS). 2. The VCS is regarded as a significant contributor to the area’s economy and a key service delivery agent. Broadly defined, it contributes about 3.8% of regional GDP and employs an estimated 4.4% of the region’s workforce. An estimated 40,000 organisations are thought to be active in the region. 3. A number of external pressures influencing the sector were identified: the need to engage with LSPs and play a full part in other local and regional networks; the need to respond to changes in governance structures; funding changes such as the end of SRB funding; and the need for strong infrastructure organisations to support the sector and enhance communication systems. 4. Contributors identified the following strengths of Blyth Valley VCS: good partnership working; dedicated volunteers; flexibility and speed of response; valuable training provision; high quality community centres; excellent community links, including involving hard to reach people; value for money; and diversity within the sector. 5. However, it was thought that the following areas could be improved upon: the relationship with the LSP; some community buildings being underused; heavy reliance on a few key staff and volunteers; structural issues, which can result in duplication of resources; heavy demands in terms of time, resources and skills; inflexible monitoring systems; the problems of short-term funding; level of social economy activity; and the need to promote the sector. 6. A number of aspirations were identified for the sector: better funding arrangements and more long-term funding; developing the infrastructure by building more centres outside Blyth town; more centralised organisational support for VCS agencies; more social economy activity, and closer working between agencies. 7. The preferred option for the future of the VCS was the development of a new infrastructure organisation that can, where appropriate, incorporate the existing infrastructure organisations and provide support to the sector as a whole. It was thought that the option of establishing this new organisation as a Development Trust should be further explored. 8. The new organisation could act as a ‘One Stop Shop’ providing advice and support on fundraising, management, human resources, health and safety, insurance, and training. It could also lend weight to funding applications; help to develop more sustainable relationships with the Council and LSP, thus freeing the Community Development Team to develop its strategic role; enhance levels of co-ordination within the sector; and develop a dedicated research facility for the sector. 9. To minimise the range of concerns expressed about how the process of change is to be managed, it is recommended that the next step should be to commission a feasibility study that will explore the various options regarding the process of change - and the establishment of the new organisation - in greater detail. 10. This report will be launched at an event held for Blyth Valley VCS in Spring 2004

A Unified and Generalized Approach to Quantum Error Correction

We present a unified approach to quantum error correction, called operator quantum error correction. This scheme relies on a generalized notion of noiseless subsystems that is not restricted to the commutant of the interaction algebra. We arrive at the unified approach, which incorporates the known techniques -- i.e. the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method -- as special cases, by combining active error correction with this generalized noiseless subsystem method. Moreover, we demonstrate that the quantum error correction condition from the standard model is a necessary condition for all known methods of quantum error correction.Comment: 5 page

Estimating Distributional Impacts of an Innovation Across Sectors in an Industry: A case study of the Australian wool industry

In this paper an approach that can be used to determine the distribution of a productivity gain on an industry is detailed. In particular, the model developed in this paper extends earlier evaluations by emphasising the crucial role of substitution between inputs across different participants in the supply chain. Crucial to any analysis of an industry are the estimates of the elasticity's of derived demand at each stage and how it changes, as the product is further refined. The wool industry is used to illustrate the effects of an innovation across sectors.Agribusiness, Production Economics,