Convergence of bimodules over maximal abelian selfadjoint algebras

We prove a continuity result for the map sending a masa-bimodule to its support. We characterise the convergence of a net of weakly closed convex hulls of bilattices in terms of the convergence of the corresponding supports, and establish a lower-semicontinuity result for the map sending a support to the corresponding masa-bimodule.

Angles in C*-algebras

In this work we characterise the C*-algebras $\mathcal{A}$ generated by projections with the property that every pair of projections in $\mathcal{A}$ has positive angle, as certain extensions of abelian algebras by algebras of compact operators. We show that this property is equivalent to a lattice theoretic property of projections and also to the property that the set of finite dimensional *-subalgebras of $\mathcal{A}$ is directed.

Multipliers of multidimensional Fourier algebras

Let $G$ be a locally compact $\sigma$-compact group. Motivated by an earlier notion for discrete groups due to Effros and Ruan, we introduce the multidimensional Fourier algebra $A^n(G)$ of $G$. We characterise the completely bounded multidimensional multipliers associated with $A^n(G)$ in several equivalent ways. In particular, we establish a completely isometric embedding of the space of all $n$-dimensional completely bounded multipliers into the space of all Schur multipliers on $G^{n+1}$ with respect to the (left) Haar measure. We show that in the case $G$ is amenable the space of completely bounded multidimensional multipliers coincides with the multidimensional Fourier-Stieltjes algebra of $G$ introduced by Ylinen. We extend some well-known results for abelian groups to the multidimensional setting.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Early Results of the 3mm Spectral Line Survey toward the L1157 B1 Shocked Region

We have conducted a sensitive 3mm observation toward the shocked region, Lynds 1157 B1, which is an interaction spot between a molecular outflow and its ambient gas. We have successfully detected the CH3CHO, HCOOCH3, and HCOOH lines, as well as the CH2DOH line. The abundances of these molecules relative to CH3OH are found to be lower than those in the low-mass star-forming core, IRAS 16293-2422. Since these molecules are thought to evaporate from grain mantles, the observational results mean that complex molecules are less abundant in grain mantles residing in the ambient cloud surrounding a prestellar/protostellar core. Instead, efficient formation of the complex organic species and deuterated species should take place in a prestellar/protostellar core. The present result verifies the importance of an unbiased line survey of this source.

A 330-360 GHz spectral survey of G34.3+0.15 - III. The outer halo

We have undertaken a 330-360 GHz molecular line survey of the halo gas surrounding the hot core associated with G34.26+0.15. In contrast to our molecular line survey of the hot core itself, where 338 lines from at least 38 species were detected, only 18 lines from 9 species were detected in the halo. The lines are mainly single transitions of simple di atomic and triatomic molecules. Lower limits to their column densities have been evaluated by an LTE method. In the case of methanol, where four transitions were detected, the rotation temperature and column density have been evaluated by the rotation diagram technique. We have modified the previous depth-dependent chemical model developed in Paper II to calculate the column densities observed along a general line of sight drawn through the model cloud. The model is also extended to produce beam-averaged column densities for better comparison with those observed. We compare the model column densities with those observed and make recommendations for future depth-dependent chemical modelling of hot cores.