A short proof of existence of disjoint hypercyclic operators

We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fr\'echet space. Similar argument provides disjoint dual hypercyclic tuples of operators of any length on any infinite dimensional Banach space with separable dual.

Operators, commuting with the Volterra operator, are not weakly supercyclic

We prove that any bounded linear operator on $L_p[0,1]$ for $1\leq p

Challenges of UK/Irish Contractors Regarding Material Management and Logistics in Confined Site Construction

The aim of this paper is to identify the various managerial issues encountered by UK/Irish contractors in the management of materials in confined urban construction sites. Through extensive literature review, detailed interviews, case studies, cognitive mapping, causal loop diagrams, questionnaire survey and documenting severity indices, a comprehensive insight into the materials management concerns within a confined construction site environment is envisaged and portrayed. The leading issues highlighted are: that contractors’ material spatial requirements exceed available space, it is difficult to coordinate the storage of materials in line with the programme, location of the site entrance makes delivery of materials particularly difficult, it is difficult to store materials on-site due to the lack of space, and difficult to coordinate the storage requirements of the various sub-contractors. With the continued development of confined urban centres and the increasing high cost of materials, any marginal savings made on-site would translate into significant monetary savings at project completion. Such savings would give developers a distinct competitive advantage in this challenging economic climate. As on-site management professionals successfully identify, acknowledge and counteract the numerous issues illustrated, the successful management of materials on a confined urban construction site becomes attainable.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Mixing operators on spaces with weak topology

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T' has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space $\omega$ due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on $\omega$, $T\oplus T$ is also hypercyclic.

On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator
semigroup $\{T_t\}_{t\geq 0}$ acting on a complex $\F$-space, every
$T_t$ with $t>0$ is supercyclic. Moreover, the set of supercyclic
vectors of $T_t$ does not depend on the choice of $t>0$.

Cyclic behaviour of Volterra composition operators

We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,
where $?$ is a measurable self-map of [0, 1]. The cyclic behaviour of $V_\phi$ is essentially determined by the behaviour of the inducing symbol $\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Design, recruitment, logistics, and data management of the GEHA (Genetics of Healthy Ageing) project

In 2004, the integrated European project GEHA (Genetics of Healthy Ageing) was initiated with the aim of identifying genes involved in healthy ageing and longevity. The first step in the project was the recruitment of more than 2500 pairs of siblings aged 90 years or more together with one younger control person from 15 areas in 11 European countries through a coordinated and standardised effort. A biological sample, preferably a blood sample, was collected from each participant, and basic physical and cognitive measures were obtained together with information about health, life style, and family composition. From 2004 to 2008 a total of 2535 families comprising 5319 nonagenarian siblings were identified and included in the project. In addition, 2548 younger control persons aged 50-75 years were recruited. A total of 2249 complete trios with blood samples from at least two old siblings and the younger control were formed and are available for genetic analyses (e.g. linkage studies and genome-wide association studies). Mortality follow-up improves the possibility of identifying families with the most extreme longevity phenotypes. With a mean follow-up time of 3.7 years the number of families with all participating siblings aged 95 years or more has increased by a factor of 5 to 750 families compared to when interviews were conducted. Thus, the GEHA project represents a unique source in the search for genes related to healthy ageing and longevity.

Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group GL(X) of invertible linear operators on a separable infinite dimensional Banach space X acts transitively on the set s (X) of countable dense linearly independent subsets of X. As a consequence, each A? s (X) is an orbit of a hypercyclic operator on X. Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space X, GL(X) acts transitively on s (X) if and only if X possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Snd ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator