Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

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.

1-amenability of A(X) for Banach spaces with 1-unconditional bases

The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property A has in fact the property. Some further ideas on the problem of whether or not amenability (in this setting) implies property A are discussed.

Sensing Spaces:A Body-oriented Architectural Design Education

The contemporary dominance of visuality has turned our understanding of space into a mode of unidirectional experience that externalizes other sensual capacities of the body while perceiving the built environment. This affects not only architectural practice but also architectural education when an introduction to the concept of space is often challenging, especially for the students who have limited spatial and sensual training. Considering that an architectural work is not perceived as a series of retinal pictures but as a repeated multi-sensory experience, the problem definitions in the design studio need to be disengaged from the dominance of a ‘focused vision’ and be re-constructed in a holistic manner. A method to address this approach is to enable the students to refer to their own sensual experiences of the built environment as a part of their design processes. This paper focuses on a particular approach to the second year architectural design teaching which has been followed in the Department of Architecture at Izmir University of Economics for the last three years. The very first architectural project of the studio and the program, entitled ‘Sensing Spaces’, is conducted as a multi-staged design process including ‘sense games, analyses of organs and their interpretations into space’. The objectives of this four-week project are to explore the sense of space through the design of a three-dimensional assembly, to create an awareness of the significance of the senses in the design process and to experiment with re-interpreted forms of bodily parts. Hence, the students are encouraged to explore architectural space through their ‘tactile, olfactory, auditory, gustative and visual stimuli’. In this paper, based on a series of examples, architectural space is examined beyond its boundaries of structure, form and function, and spatial design is considered as an activity of re-constructing the built environment through the awareness of bodily senses.

The spaces of knowledge: Contributions towards a historical geography of science

Reprinted in Trevor Barnes and Derek Gregory (eds), Reading Human Geography: The Poetics and Politics of Inquiry, (London: Arnold, 1997), pp. 27-48

Perceiving and acting upon spaces in a VR rugby task: Expertise effects in affordance detection and task achievement

This study used a virtual simulated 3vs3 rugby task to investigate whether gaps opening in particular running channels promote different actions by the ball-carrier player and whether an effect of rugby expertise is verified. We manipulated emergent gaps in three different locations: gap1 in the participant’s own running channel, gap 2 in the 1st receiver's running channel, and gap3 in the 2nd receiver's running channel. Recreational, intermediate, professional and non-rugby players performed the task. They could i) run with the ball, ii) make a short pass, or iii) make a long pass. All actions were digitally recorded. Results revealed that the emergence of gaps in the defensive line with respect to the participant’s own position significantly influenced action selection. Namely, ‘run’ was most often the action performed in gap 1, ‘short pass’ in gap 2, and ‘long pass’ in gap 3 trials. Furthermore, a strong positive relationship between expertise and task achievement was found.

“Voices, Spaces and Processes in Constitutionalism - Editorial"

(With C. Harvey, J. Shaw .)

A Kernel Interleaved Scheduling Method for Streaming Applications on Soft-core Vector Processors

Massively parallel networks of highly efficient, high performance Single Instruction Multiple Data (SIMD) processors have been shown to enable FPGA-based implementation of real-time signal processing applications with performance and
cost comparable to dedicated hardware architectures. This is achieved by exploiting simple datapath units with deep processing pipelines. However, these architectures are highly susceptible to pipeline bubbles resulting from data and control hazards; the only way to mitigate against these is manual interleaving of
application tasks on each datapath, since no suitable automated interleaving approach exists. In this paper we describe a new automated integrated mapping/scheduling approach to map algorithm tasks to processors and a new low-complexity list scheduling technique to generate the interleaved schedules. When applied to a spatial Fixed-Complexity Sphere Decoding (FSD) detector
for next-generation Multiple-Input Multiple-Output (MIMO) systems, the resulting schedules achieve real-time performance for IEEE 802.11n systems on a network of 16-way SIMD processors on FPGA, enable better performance/complexity balance than current approaches and produce results comparable to handcrafted implementations.