A Lindenstrauss theorem for some classes of multilinear mappings

Under some natural hypotheses, we show that if a multilinear mapping belongs to some Banach multlinear ideal, then it can be approximated by multilinear mappings belonging to the same ideal whose Arens extensions simultaneously attain their norms. We also consider the class of symmetric multilinear mappings.Comment: 11 page

Decomposable symmetric mappings between infinite-dimensional spaces

Decomposable mappings from the space of symmetric k-fold tensors over E, O×s,kE, to the space of k-fold tensors over F, O×s,kF, are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable mapping belongs to a given operator ideal, then so does its inducing operator. This result allows us to classify injective linear operators between spaces of homogeneous approximable polynomials and between spaces of nuclear polynomials which map rank-1 polynomials to rank-1 polynomials. © 2007 Institut Mittag-Leffler.Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina

Astrometric performance of the Gemini multi-conjugate adaptive optics system in crowded fields

The Gemini Multi-conjugate adaptive optics System (GeMS) is a facility instrument for the Gemini-South telescope. It delivers uniform, near-diffraction-limited image quality at near-infrared wavelengths over a 2 arcminute field of view. Together with the Gemini South Adaptive Optics Imager (GSAOI), a near-infrared wide field camera, GeMS/GSAOI's combination of high spatial resolution and a large field of view will make it a premier facility for precision astrometry. Potential astrometric science cases cover a broad range of topics including exo-planets, star formation, stellar evolution, star clusters, nearby galaxies, black holes and neutron stars, and the Galactic center. In this paper, we assess the astrometric performance and limitations of GeMS/GSAOI. In particular, we analyze deep, mono-epoch images, multi-epoch data and distortion calibration. We find that for single-epoch, un-dithered data, an astrometric error below 0.2 mas can be achieved for exposure times exceeding one minute, provided enough stars are available to remove high-order distortions. We show however that such performance is not reproducible for multi-epoch observations, and an additional systematic error of ~0.4 mas is evidenced. This systematic multi-epoch error is the dominant error term in the GeMS/GSAOI astrometric error budget, and it is thought to be due to time-variable distortion induced by gravity flexure.Comment: 16 pages, 22 figures, accepted for publication in MNRA

Jack vertex operators and realization of Jack functions

We give an iterative method to realize general Jack functions from Jack functions of rectangular shapes. We first show some cases of Stanley's conjecture on positivity of the Littlewood-Richardson coefficients, and then use this method to give a new realization of Jack functions. We also show in general that vectors of products of Jack vertex operators form a basis of symmetric functions. In particular this gives a new proof of linear independence for the rectangular and marked rectangular Jack vertex operators. Thirdly a generalized Frobenius formula for Jack functions was given and was used to give new evaluation of Dyson integrals and even powers of Vandermonde determinant.Comment: Expanded versio

Ancestral genome estimation reveals the history of ecological diversification in Agrobacterium

Horizontal gene transfer (HGT) is considered as a major source of innovation in bacteria, and as such is expected to drive adaptation to new ecological niches. However, among the many genes acquired through HGT along the diversification history of genomes, only a fraction may have actively contributed to sustained ecological adaptation. We used a phylogenetic approach accounting for the transfer of genes (or groups of genes) to estimate the history of genomes in Agrobacterium biovar 1, a diverse group of soil and plant-dwelling bacterial species. We identified clade-specific blocks of cotransferred genes encoding coherent biochemical pathways that may have contributed to the evolutionary success of key Agrobacterium clades. This pattern of gene coevolution rejects a neutral model of transfer, in which neighboring genes would be transferred independently of their function and rather suggests purifying selection on collectively coded acquired pathways. The acquisition of these synapomorphic blocks of cofunctioning genes probably drove the ecological diversification of Agrobacterium and defined features of ancestral ecological niches, which consistently hint at a strong selective role of host plant rhizospheres

Intersecting where? The multi-scalar contextual embeddedness of intersectional entrepreneurs

We explore the experiences of LGBT* ethnic minority entrepreneurs, their changing locations and their entrepreneurial activities. Using a unique mixed-method approach which collected empirical data from Germany and the Netherlands, the paper combines an ethnographic fieldwork of intersectional entrepreneurs, community activists and policy-makers with an original survey with LGBT* customers. Our findings contribute to understanding of intersectionality by revealing the role played by the contextualized embeddedness of intersectional entrepreneurs at the different geographic scales of supranational, national, regional and inter and intra-urban. While such embeddedness frames the challenges they face, it also provides opportunities for intersectional entrepreneurs. Using a multi-scalar perspective, this paper delivers a spatially contextual perspective of entrepreneurial diversity and provides a framework to analyse the complex issues and contexts with which intersectional entrepreneurs are both confronted and embedded within. This paper contributes to refining the spatial context of entrepreneurship which has gained attention in recent studies of entrepreneurship and regional development. The paper responds to a call for gender entrepreneurship scholars to contribute to understanding of intersectional entrepreneurship. Finally, this study goes beyond the binary view of female migrant entrepreneurship by adopting a more gender diverse lens which considers the experiences of LGBT* entrepreneurs from ethnic minorities

Spectra of weighted algebras of holomorphic functions

We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to investigate how their induced mappings act on the analytic structure of the spectrum. Moreover, a Banach-Stone type question is addressed.Comment: 25 pages Corrected typo

Quantum Calogero-Moser Models: Integrability for all Root Systems

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack polynomials are defined for all root systems as unique eigenfunctions of the Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v) Algebraic construction of all excited states in terms of creation operators. These are mainly generalisations of the results known for the models based on the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure