35,017 research outputs found

    Confluent operator algebras and the closability property

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    Certain operator algebras A on a Hilbert space have the property that every densely defined linear transformation commuting with A is closable. Such algebras are said to have the closability property. They are important in the study of the transitive algebra problem. More precisely, if A is a two-transitive algebra with the closability property, then A is dense in the algebra of all bounded operators, in the weak operator topology. In this paper we focus on algebras generated by a completely nonunitary contraction, and produce several new classes of algebras with the closability property. We show that this property follows from a certain strict cyclicity property, and we give very detailed information on the class of completely nonunitary contractions satisfying this property, as well as a stronger property which we call confluence.Comment: Preliminary versio

    Experimental investigation of thermal annealing of nuclear-reactor-induced coloration in fused silica

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    Spectral transmission characteristics of fused silica over range of temperature prior to nuclear irradiation and during thermal annealing of reactor-induced coloratio

    Applications of Hilbert Module Approach to Multivariable Operator Theory

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    A commuting nn-tuple (T1,…,Tn)(T_1, \ldots, T_n) of bounded linear operators on a Hilbert space \clh associate a Hilbert module H\mathcal{H} over C[z1,…,zn]\mathbb{C}[z_1, \ldots, z_n] in the following sense: C[z1,…,zn]×H→H,(p,h)↦p(T1,…,Tn)h,\mathbb{C}[z_1, \ldots, z_n] \times \mathcal{H} \rightarrow \mathcal{H}, \quad \quad (p, h) \mapsto p(T_1, \ldots, T_n)h,where p∈C[z1,…,zn]p \in \mathbb{C}[z_1, \ldots, z_n] and h∈Hh \in \mathcal{H}. A companion survey provides an introduction to the theory of Hilbert modules and some (Hilbert) module point of view to multivariable operator theory. The purpose of this survey is to emphasize algebraic and geometric aspects of Hilbert module approach to operator theory and to survey several applications of the theory of Hilbert modules in multivariable operator theory. The topics which are studied include: generalized canonical models and Cowen-Douglas class, dilations and factorization of reproducing kernel Hilbert spaces, a class of simple submodules and quotient modules of the Hardy modules over polydisc, commutant lifting theorem, similarity and free Hilbert modules, left invertible multipliers, inner resolutions, essentially normal Hilbert modules, localizations of free resolutions and rigidity phenomenon. This article is a companion paper to "An Introduction to Hilbert Module Approach to Multivariable Operator Theory".Comment: 46 pages. This is a companion paper to arXiv:1308.6103. To appear in Handbook of Operator Theory, Springe

    High levels of gene flow and genetic diversity in Irish populations of Salix caprea L. inferred from chloroplast and nuclear SSR markers

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    peer-reviewedBackground Salix caprea is a cold-tolerant pioneer species that is ecologically important in Europe and western and central Asia. However, little data is available on its population genetic structure and molecular ecology. We describe the levels of geographic population genetic structure in natural Irish populations of S. caprea and determine the extent of gene flow and sexual reproduction using both chloroplast and nuclear simple sequence repeats (SSRs). Results A total of 183 individuals from 21 semi-natural woodlands were collected and genotyped. Gene diversity across populations was high for the chloroplast SSRs (H T  = 0.21-0.58) and 79 different haplotypes were discovered, among them 48% were unique to a single individual. Genetic differentiation of populations was found to be between moderate and high (mean G ST  = 0.38). For the nuclear SSRs, G ST was low at 0.07 and observed heterozygosity across populations was high (H O  = 0.32-0.51); only 9.8% of the genotypes discovered were present in two or more individuals. For both types of markers, AMOVA showed that most of the variation was within populations. Minor geographic pattern was confirmed by a Bayesian clustering analysis. Gene flow via pollen was found to be approximately 7 times more important than via seeds. Conclusions The data are consistent with outbreeding and indicate that there are no significant barriers for gene flow within Ireland over large geographic distances. Both pollen-mediated and seed-mediated gene flow were found to be high, with some of the populations being more than 200 km apart from each other. These findings could simply be due to human intervention through seed trade or accidental transportation of both seeds and pollen. These results are of value to breeders wishing to exploit natural genetic variation and foresters having to choose planting material.Teagasc Walsh Fellowship Programm
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