8 research outputs found

    M-structures in vector-valued polynomial spaces

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    This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; F), is an M-ideal in the space of continuous n-homogeneous polynomials P(nE; F). We show that there is some hope for this to happen only for a finite range of values of n. We establish sufficient conditions under which the problem has positive and negative answers and use the obtained results to study the particular cases when E = lp and F = lq or F is a Lorentz sequence space d(w; q). We extend to our setting the notion of property (M) introduced by Kalton which allows us to lift M-structures from the linear to the vector-valued polynomial context. Also, when Pw(nE; F) is an M-ideal in P(nE; F) we prove a Bishop-Phelps type result for vector-valued polynomials and relate norm-attaining polynomials with farthest points and remotal sets.Fil: Dimant, Veronica Isabel. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

    Ideal structures in vector-valued polynomial spaces

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    This paper is concerned with the study of geometric structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of n-homogeneous polynomials, Pw(nE,F), which are weakly continuous on bounded sets, is an HB-subspace or an M(1,C)-ideal in the space of continuous n-homogeneous polynomials, P(nE,F). We establish sufficient conditions under which the problem can be positively solved. Some examples are given. We also study when some ideal structures pass from Pw(nE,F) as an ideal in P(nE,F) to the range space F as an ideal in its bidual F∗∗.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; ArgentinaFil: Prieto, Angeles. Universidad Complutense de Madrid; Españ

    Gleason parts for algebras of holomorphic functions in infinite dimensions

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    For a complex Banach space X with open unit ball BX, consider the Banach algebras H∞(BX) of bounded scalar-valued holomorphic functions and the subalgebra Au(BX) of uniformly continuous functions on BX. Denoting either algebra by A, we study the Gleason parts of the set of scalar-valued homomorphisms M(A) on A. Following remarks on the general situation, we focus on the case X= c, giving a complete characterization of the Gleason parts of M(Au(Bc0)) and, among other things, showing that every fiber in M(H∞(Bc0)) over a point in Bℓ∞ contains 2 c discs lying in different Gleason parts.Fil: Aron, Richard Martin. Kent State University; Estados UnidosFil: Dimant, Veronica Isabel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Lassalle, Silvia Beatriz. Universidad de San Andrés; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Maestre, Manuel. Universidad de Valencia; Españ

    Neuroanatomical distribution of angiotensin-II-like neuropeptide within the central nervous system of the crab <i>Chasmagnathus</i>; physiological changes triggered by water deprivation

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    The angiotensins constitute a neuropeptidergic system that emerged early in evolution. Their classical osmoregulatory and dipsogenic functions and their mnemonic actions have been demonstrated both in vertebrates and in some invertebrates. Previously, we have shown that, in the euryhaline and semiterrestrial crab Chasmagnathus granulatus, water deprivation correlates with an increased level of brain angiotensin-II-like neuropeptide/s (ANGII-like) and improves memory processes through ANGII receptors. We have proposed that the release of brain angiotensins in response to water shortages is an ancient mechanism for coordinating various functions that, together, enable organisms to tolerate this environmental change. Here, we have evaluated the physiological changes in ANGII-like levels in diverse structures of the central nervous system of these animals during water deprivation. The neuroanatomical distribution of ANGII-like is described in the optic lobes and brain of Chasmagnathus granulatus and the physiological changes in ANGII-like distribution in various brain neuropils is evaluated after water deprivation. Our results indicate that ANGII-like is widely distributed, especially in the medial protocerebrum. After 2 h of water deprivation, ANGII-like immunoreactivity increases in the central body and decreases in the olfactory neuropil and, after 6 h of water deprivation, is markedly reduced in several brain areas. Although further experiments are needed to establish that the angiotensinergic system is involved in the balance of body fluids in this crab, our results suggest that ANGII regulates several functions during water shortages.Facultad de Ciencias Veterinaria
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