Factorization in commutative Banach algebras

We consider when a (non-unital) commutative Banach algebra has a variety of factorization properties; we list the (obvious) implications between these properties, and then investigate whether any of these implications can be reversed in various classes of commutative Banach algebras. We summarize the known counter-examples to these possible reverse implications, and add further counter-examples. Some results are used to show the existence of a large family of prime ideals in each non-zero, commutative, radical Banach algebra with a dense set of products

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic

Shift invariant preduals of ℓ₁(ℤ)

The Banach space ℓ<sub>1</sub>(ℤ) admits many non-isomorphic preduals, for example, C(K) for any compact countable space K, along with many more exotic Banach spaces. In this paper, we impose an extra condition: the predual must make the bilateral shift on ℓ<sub>1</sub>(ℤ) weak<sup>*</sup>-continuous. This is equivalent to making the natural convolution multiplication on ℓ<sub>1</sub>(ℤ) separately weak*-continuous and so turning ℓ<sub>1</sub>(ℤ) into a dual Banach algebra. We call such preduals <i>shift-invariant</i>. It is known that the only shift-invariant predual arising from the standard duality between C<sub>0</sub>(K) (for countable locally compact K) and ℓ<sub>1</sub>(ℤ) is c<sub>0</sub>(ℤ). We provide an explicit construction of an uncountable family of distinct preduals which do make the bilateral shift weak<sup>*</sup>-continuous. Using Szlenk index arguments, we show that merely as Banach spaces, these are all isomorphic to c<sub>0</sub>. We then build some theory to study such preduals, showing that they arise from certain semigroup compactifications of ℤ. This allows us to produce a large number of other examples, including non-isometric preduals, and preduals which are not Banach space isomorphic to c<sub>0</sub>

Effects of air pollution and the introduction of the London Low Emission Zone on the prevalence of respiratory and allergic symptoms in schoolchildren in East London: a sequential cross-sectional study

The adverse effects of traffic-related air pollution on children’s respiratory health have been widely reported, but few studies have evaluated the impact of traffic-control policies designed to reduce urban air pollution. We assessed associations between traffic-related air pollutants and respiratory/allergic symptoms amongst 8–9 year-old schoolchildren living within the London Low Emission Zone (LEZ). Information on respiratory/allergic symptoms was obtained using a parent-completed questionnaire and linked to modelled annual air pollutant concentrations based on the residential address of each child, using a multivariable mixed effects logistic regression analysis. Exposure to traffic-related air pollutants was associated with current rhinitis: NOx (OR 1.01, 95% CI 1.00–1.02), NO2 (1.03, 1.00–1.06), PM10 (1.16, 1.04–1.28) and PM2.5 (1.38, 1.08–1.78), all per μg/m3 of pollutant, but not with other respiratory/allergic symptoms. The LEZ did not reduce ambient air pollution levels, or affect the prevalence of respiratory/allergic symptoms over the period studied. These data confirm the previous association between traffic-related air pollutant exposures and symptoms of current rhinitis. Importantly, the London LEZ has not significantly improved air quality within the city, or the respiratory health of the resident population in its first three years of operation. This highlights the need for more robust measures to reduce traffic emissions

Campus Mental Health: Implications for Instructors Supporting Students

The recent escalation in student suicides due to mental health problems has encouraged higher education institutions to not only modify their overall support structures, but to also (re)define the role of faculty and staff. Despite the increased attention given to student mental health in Canadian higher education institutions, little is known and understood about how instructors view their role as supporters or promoters of student mental health. The purpose of this study was to explore the role of college instructors in supporting students with mental health problems or illnesses. Participants were 42 instructors between the ages of 25 to 64 from Molize College in Toronto, Ontario. Qualitative ethnography was employed to gather data from participants, specifically through a survey questionnaire and interviews. A constructivist framework was adopted to analyze and understand the values, perceptions, meanings, and practices post-secondary instructors carry around notions of student mental health and intervention. Findings revealed that instructors were generally aware of student mental health concerns in post-secondary institutions, but that greater awareness was still warranted, namely in the areas of instructor mental health and location of support services. Findings also demonstrated that most instructors evaluated their knowledge and confidence in relation to student mental health as poor, which was often credited to limited relevant professional development and training. Additionally, data indicated that instructors carried skepticism towards the role of some student support services departments, as well as towards their own role when supporting the mental health and well-being of students. On a final note, findings revealed that instructors commonly employed four practices to support the mental health and well-being of students: conversation, referral, accommodations, and curricular inclusion and instruction. Future studies are encouraged to acknowledge the narratives of instructors through ethnographic inquiry, to allow for greater insights into their awareness, knowledge/confidence, responsibilities, and practices when it comes to supporting the mental health and well-being of students in higher education settings. Incorporating the instructor may not be a panacea for the shortcomings of current mental health policies and practices in higher education settings, but it can certainly represent a colossal step in that direction. KEYWORDS: student mental health, higher education, instructor

Fragranced consumer products: effects on asthmatic Australians

Exposure to fragranced consumer products, such as air fresheners and cleaning supplies, is associated with adverse health effects such as asthma attacks, breathing difficulties, and migraine headaches. This study investigated the prevalence and types of health problems associated with exposure to fragranced products among asthmatic Australians. Nationally representative cross-sectional data were obtained in June 2016 with an online survey of adult Australians (n = 1098), of which 28.5% were medically diagnosed with asthma or an asthma-like condition. Nationally, 55.6% of asthmatics, and 23.9% of non-asthmatics, report adverse health effects after exposure to fragranced products. Specifically, 24.0% of asthmatics report an asthma attack. Moreover, 18.2% of asthmatics lost workdays or a job in the past year due to fragranced products in the workplace. Over 20% of asthmatics are unable to access public places and restrooms that use air fresheners. Exposure to fragranced products is associated with health problems, some potentially serious, in an estimated 2.2 million asthmatic adult Australians. Asthmatics were proportionately more affected than non-asthmatics (prevalence odds ratio 3.98; 95% confidence interval 3.01–5.24). Most asthmatics would prefer workplaces, healthcare facilities, and environments that are fragrance-free, which could help reduce adverse effects

EPA guidance on the role and responsibilities of psychiatrists

Psychiatry is that branch of the medical profession, which deals with the origin, diagnosis, prevention, and management of mental disorders or mental illness, emotional and behavioural disturbances. Thus, a psychiatrist is a trained doctor who has received further training in the field of diagnosing and managing mental illnesses, mental disorders and emotional and behavioural disturbances. This EPA Guidance document was developed following consultation and literature searches as well as grey literature and was approved by the EPA Guidance Committee. The role and responsibilities of the psychiatrist include planning and delivering high quality services within the resources available and to advocate for the patients and the services. The European Psychiatric Association seeks to rise to the challenge of articulating these roles and responsibilities. This EPA Guidance is directed towards psychiatrists and the medical profession as a whole, towards other members of the multidisciplinary teams as well as to employers and other stakeholders such as policy makers and patients and their families