Jordan weak amenability and orthogonal forms on JB*-algebras

We prove the existence of a linear isometric correspondence between the Banach space of all symmetric orthogonal forms on a JB$^*$-algebra $\mathcal{J}$ and the Banach space of all purely Jordan generalized derivations from $\mathcal{J}$ into $\mathcal{J}^*$. We also establish the existence of a similar linear isometric correspondence between the Banach spaces of all anti-symmetric orthogonal forms on $\mathcal{J}$, and of all Lie Jordan derivations from $\mathcal{J}$ into $\mathcal{J}^*$

LOCALLY AND COLOCALLY FACTORABLE BANACH SPACES

We generalize the concept of locality (resp. colocality) to the concept of locally factorable (resp. colocally factorable) such that Theorem 2 of [2] and Theorems 1.7 and 1.16 of [11] are still valid for the new concepts. In addition we show that locally factorable and colocally factorable are inherited by complemented subspace, then we present some examples and establish relations between locally factorable and colocally factorable. We prove some relations between being finitely (resp. cofinitely) represented in a Banach space and being locally factorable (resp. colocally factorable) some family of finite dimensional Banach spaces.</p

Surgical trainee research collaboratives in the UK: an observational study of research activity and publication productivity.

OBJECTIVES: To analyse the research activity and publication output of surgical trainee research collaboratives in the UK. SETTING: Surgical trainee research collaboratives in the UK. PARTICIPANTS: A total of 24 collaboratives were included in this study from 33 identified organisations. We excluded one group that focused purely on systematic review of the literature and eight groups for which we could not identify suitable data sources (website or trainee committee contact). PRIMARY AND SECONDARY OUTCOME: Primary data-points were identified for each collaborative including surgical subspeciality, numbers and types of projects. For published articles, secondary outcomes including study population size, journal impact factor, number of citations and evidence level were collected. RESULTS: A total of 24 collaboratives met our inclusion criteria with a portfolio of 80 projects. The project types included audit (46%), randomised clinical trial (16%), surveys (16%), cohort studies (10%), systematic reviews (2.5%) and other or unidentifiable (9.5%). A total of 35 publications were identified of which just over half (54%) were original research articles. The median size of studied population was 540 patients with a range from 108 to 3138. The published works provided a varied compilation of evidence levels ranging from 1b (individual RCT) to 5 (expert opinion) with a median level of 2b (individual cohort study). The West Midlands Research Collaborative had the highest number of publications (13), citations (130) and h-index (5). CONCLUSIONS: The experience of UK-based trainee research collaboratives provides useful insights for trainees and policymakers in global healthcare systems on the value and feasibility of trainee-driven high quality surgical research.AABJ is funded by the Wellcome Trust (grant number R43608). PJH is supported by the National Institute for Health Research (NIHR) Cambridge Biomedical Research Centre and by an NIHR Research Professorship.This is the final version of the article. It first appeared from BMJ Publishing Group via http://dx.doi.org/10.1136/bmjopen-2015-01037