On local properties of Hochschild cohomology of a C∗^*- algebra

Let $A$ be a C$^*$-algebra, and let $X$ be a Banach $A$-bimodule. B. E. Johnson showed that local derivations from $A$ into $X$ are derivations. We extend this concept of locality to the higher cohomology of a $C^*$-algebra %for $n$-cocycles from $A^{(n)}$ into $X$ and show that, for every $n\in \N$, bounded local $n$-cocycles from $A^{(n)}$ into $X$ are $n$-cocycles.Comment: 13 page

Multi-normed spaces

We modify the very well known theory of normed spaces (E, \norm) within functional analysis by considering a sequence (\norm_n : n\in\N) of norms, where \norm_n is defined on the product space $E^n$ for each $n\in\N$. Our theory is analogous to, but distinct from, an existing theory of `operator spaces'; it is designed to relate to general spaces $L^p$ for $p\in [1,\infty]$, and in particular to $L^1$-spaces, rather than to $L^2$-spaces. After recalling in Chapter 1 some results in functional analysis, especially in Banach space, Hilbert space, Banach algebra, and Banach lattice theory that we shall use, we shall present in Chapter 2 our axiomatic definition of a `multi-normed space' ((E^n, \norm_n) : n\in \N), where (E, \norm) is a normed space. Several different, equivalent, characterizations of multi-normed spaces are given, some involving the theory of tensor products; key examples of multi-norms are the minimum and maximum multi-norm based on a given space. Multi-norms measure `geometrical features' of normed spaces, in particular by considering their `rate of growth'. There is a strong connection between multi-normed spaces and the theory of absolutely summing operators. A substantial number of examples of multi-norms will be presented. Following the pattern of standard presentations of the foundations of functional analysis, we consider generalizations to `multi-topological linear spaces' through `multi-null sequences', and to `multi-bounded' linear operators, which are exactly the `multi-continuous' operators. We define a new Banach space ${\mathcal M}(E,F)$ of multi-bounded operators, and show that it generalizes well-known spaces, especially in the theory of Banach lattices. We conclude with a theory of `orthogonal decompositions' of a normed space with respect to a multi-norm, and apply this to construct a `multi-dual' space.Comment: Many update

Approximately multiplicative maps from weighted semilattice algebras

We investigate which weighted convolution algebras $\ell^1_\omega(S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson (JLMS, 1986). We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, as are all $\ell^1_\omega(S)$ where $S$ has either finite width or finite height. Some of these finite-width examples are isomorphic to function algebras studied by Feinstein (IJMMS, 1999). We also investigate when $(\ell^1_\omega(S),{\bf M}_2)$ is an AMNM pair in the sense of Johnson (JLMS, 1988), where ${\bf M}_2$ denotes the algebra of 2-by-2 complex matrices. In particular, we obtain the following two contrasting results: (i) for many non-trivial weights on the totally ordered semilattice ${\bf N}_{\min}$, the pair $(\ell^1_\omega({\bf N}_{\min}),{\bf M}_2)$ is not AMNM; (ii) for any semilattice $S$, the pair $(\ell^1(S),{\bf M}_2)$ is AMNM. The latter result requires a detailed analysis of approximately commuting, approximately idempotent $2\times 2$ matrices.Comment: AMS-LaTeX. v3: 31 pages, additional minor corrections to v2. Final version, to appear in J. Austral. Math. Soc. v4: small correction of mis-statement at start of Section 4 (this should also be fixed in the journal version

Approximate characterizations of projectivity and injectivity for Banach modules

We characterize projective and injective Banach modules in approximate terms, generalizing thereby a characterization of contractible Banach algebras given by F. Ghahramani and R. J. Loy. As a corollary, we show that each uniformly approximately amenable Banach algebra is amenable. Some applications to homological dimensions of Banach modules and algebras are also given.Comment: 12 page

Ultrapowers of Banach algebras and modules

The Arens products are the standard way of extending the product from a Banach algebra \mc A to its bidual \mc A''. Ultrapowers provide another method which is more symmetric, but one that in general will only give a bilinear map, which may not be associative. We show that if \mc A is Arens regular, then there is at least one way to use an ultrapower to recover the Arens product, a result previously known for C$^*$-algebras. Our main tool is a Principle of Local Reflexivity result for modules and algebras.Comment: 17 page

Controlling insect pests of stored products using insect growth regulators and insecticides of microbial origin (NRI Bulletin 64)

The identification of alternatives to synthetic contact insecticides for the protection of durable foodstuffs has become a focus for research worldwide during the last 15 years. Candidate materials have included plants and plant extracts, inert dusts, insect growth regulators (IGRs) and microbial insecticides. The aim has been to find products to replace or enhance current control methods which rely on fumigation and insecticide application. Progress of research into the use of IGRs and microbial insecticides is reviewed. So far, only methoprene and Bacillus thuringiensis have been approved for application; details of their current uses are described. Other candidate materials are either still at the early stages of evaluation, or have been discarded because their levels of persistence are too high. In these cases, results from both laboratory and field trials are outlined. A few materials which have shown potential against agricultural, medical or veterinary insect pests have been included as they may be tested against storage pests in the future. Recent experience with fenoxycarb has indicated that prolonged persistence may render some materials unsuitable for use on stored foodstuffs. Inclusion of a material in this review does not imply its recommendation as a grain protectant. Novel insecticides are subject to the same stringent regulations as other pesticides, and their eventual approval will be a long and costly exercise. It is concluded that although IGRs and microbial insecticides show considerable potential for the protection of stored products, further research is needed

Doctor and new patient communication : the influence of a priori assumptions

PhD ThesisDoctor-patient communication is fundamental to the therapeutic relationship necessary to achieve mutual understanding of the implications and impact of illness, diagnostic and treatment decisions, and health outcomes. It is recognised that both patient and doctor come with their own perspectives, beliefs and agendas. This quasi-ethnographic study explores the influence of the doctor’s own a priori assumptions on their communication with a new patient. Methods Cognitive interviewing was used prior to consultations to explore the doctor’s thoughts triggered by the referral information. The relevant subsequent consultations were audio recorded, as were loosely structured interviews after the consultation, during which the doctor reflected on what had been said and why. All data was subjected to qualitative thematic analysis. Conclusion The source, content and format of referrals are significant and doctors approach the information about the patient with their own perspectives, beliefs and experiences. The existence of assumptions and stereotypes appear to be triggered when processing the information. Doctors begin to develop the communication with the patient, based on their expectations of themselves and of the patient, before the patient is seen. During the consultation, some a priori assumptions were observed to be significant. A priori assumptions are influential to the communication with the patient and can result in communication not anticipated by the clinician. The relationship achieved with the patient during the consultation can be understood in the context of the concepts of recognition and presence