Factorization of weakly continuous holomorphic mappings

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping $f$ between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form $f=g\circ S$, where $S$ is a compact operator and $g$ a holomorphic mapping

The role of meta-cognitions and thought control techniques in predisposition to auditory and visual hallucinations

Objectives. This study examines the relationship between a predisposition to hallucinations and meta-cognitive variables and thought-control techniques, controlling for the possible effect of anxiety. In order to do so, we start out with the hypothesis that anxiety does not, in itself, explain the association between meta-cognitions and a predisposition to auditory and visual hallucinations. Design. A within-participants correlational design was employed. Methods. Four psychometric tests relating to predisposition to hallucinations, anxiety, meta-cognitions and thought-control techniques were administered to 150 participants. Results. It was found that, after controlling for participants' anxiety levels, the ‘loss of cognitive confidence’ factor predicted the score on the scale of predisposition to both auditory and visual hallucinations. Thought-control strategies based on worry were also found to be predictive of a greater predisposition to hallucinations, regardless of whether or not participants' anxiety level was controlled. Conclusions. Meta-cognitive variables of cognitive confidence and thought control through worry are positively associated with a predisposition to hallucinations. Limitations. The correlational nature of the design does not allow inferences about causal relationships