Toeplitz operators with distributional symbols on Bergman spaces

We study the boundedness and compactness of Toeplitz operators Ta on Bergman spaces , 1 < p < ∞. The novelty is that we allow distributional symbols. It turns out that the belonging of the symbol to a weighted Sobolev space of negative order is sufficient for the boundedness of Ta. We show the natural relation of the hyperbolic geometry of the disc and the order of the distribution. A corresponding sufficient condition for the compactness is also derived.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Rigid body trajectories in different 6D spaces

The objective of this paper is to show that the group SE(3) with an imposed Lie-Poisson structure can be used to determine the trajectory in a spatial frame of a rigid body in Euclidean space. Identical results for the trajectory are obtained in spherical and hyperbolic space by scaling the linear displacements appropriately since the influence of the moments of inertia on the trajectories tends to zero as the scaling factor increases. The semidirect product of the linear and rotational motions gives the trajectory from a body frame perspective. It is shown that this cannot be used to determine the trajectory in the spatial frame. The body frame trajectory is thus independent of the velocity coupling. In addition, it is shown that the analysis can be greatly simplified by aligning the axes of the spatial frame with the axis of symmetry which is unchanging for a natural system with no forces and rotation about an axis of symmetry.

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

Performance evaluation of wall mounted convector for pre-heating naturally ventilated spaces

This paper presents the results of performance monitoring under real winter weather conditions, controlled laboratory testing and computational fluid dynamics (CFD) analysis of a wall mounted ventilation air inlet heat convector. For real winter weather monitoring, the wall-mounted convector was installed in a laboratory room of the Engineering Building of the School of Construction Management and Engineering. Air and hot water temperatures and air speeds were measured at the entrance to the convector and in the room. The hot water temperature was controlled at 40, 60 and 80 °C. The monitoring results were later used as boundary conditions for a CFD simulation to investigate the air movement in the room. Controlled laboratory testing was conducted in laboratories at the University of Reading, UK and at Wetterstad Consultancy, Sweden. The results of the performance investigation showed that the system contributed greatly to the room heating, particularly at a water temperature of 80 °C. Also adequate fresh air was supplied to the room. Such a system is able to provide an energy efficient method of eliminating problems associated with cold winter draughts.

Coordinated management of intelligent pervasive spaces

The content of this paper is a snapshot of a current project looking at producing a real-time sensor-based building assessment tool, and a system that personalises workspaces using multi-agent technology. Both systems derive physical environment information from a wireless sensor network that allows clients to subscribe to real-time sensed data. The principal ideologies behind this project are energy efficiency and well-being of occupants; in the context of leveraging the current state-of-the-art in agent technology, wireless sensor networks and building assessment systems to enable the optimisation and assessment of buildings. Participants of this project are from both industry (construction and research) and academia.