112 research outputs found

    Bounded holomorphic functions attaining their norms in the bidual

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    Under certain hypotheses on the Banach space XX, we prove that the set of analytic functions in Au(X)\mathcal{A}_u(X) (the algebra of all holomorphic and uniformly continuous functions in the ball of XX) whose Aron-Berner extensions attain their norms, is dense in Au(X)\mathcal{A}_u(X). The result holds also for functions with values in a dual space or in a Banach space with the so-called property (β)(\beta). For this, we establish first a Lindenstrauss type theorem for continuous polynomials. We also present some counterexamples for the Bishop-Phelps theorem in the analytic and polynomial cases where our results apply.Comment: Accepted in Publ. Res. Inst. Math. Sc

    Strong subdifferentiability and local Bishop–Phelps–Bollobás properties

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    Some local versions of the Bishop–Phelps–Bollobás property for operators have been recently presented in Dantas et al. (J Math Anal Appl 468(1):304–323, 2018). In the present article, we continue studying these properties for multilinear mappings. We show some differences between the local and uniform versions of these and also provide some interesting examples which show that this study is not just a mere generalization of the linear case. As a consequence of our results, we get that, for 2 < p, q< ∞, the norm of the projective tensor product ℓp⊗ ^ πℓq is strongly subdifferentiable. Moreover, we present necessary and sufficient conditions for the norm of a Banach space Y to be strongly subdifferentiable through the study of these properties for bilinear mappings on ℓ1N×Y.Fil: Dantas, Sheldon. Czech Technical University in Prague; República ChecaFil: Kim, Sun Kwang. Chungbuk National University; Corea del SurFil: Lee, Han Ju. Dongguk University, Seoul; Corea del SurFil: Mazzitelli, Martin Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Universidad Nacional de Cuyo; Argentina. Comisión Nacional de Energía Atómica. Fundación José A. Balseiro; Argentin

    Renormalization in theories with modified dispersion relations: weak gravitational fields

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    We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein-Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of and , working in the weak field approximation. We show that for dispersion relations containing up to 2s2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on ss in a qualitatively different way: while becomes convergent for a sufficiently large value of ss, the number of divergent terms in the adiabatic expansion of increases with ss. This property was not apparent in previous results for spatially homogeneous backgrounds.Comment: 12 pages, no figure

    Soluble models in 2d dilaton gravity

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    A one-parameter class of simple models of two-dimensional dilaton gravity, which can be exactly solved including back-reaction effects, is investigated at both classical and quantum levels. This family contains the RST model as a special case, and it continuously interpolates between models having a flat (Rindler) geometry and a constant curvature metric with a non-trivial dilaton field. The processes of formation of black hole singularities from collapsing matter and Hawking evaporation are considered in detail. Various physical aspects of these geometries are discussed, including the cosmological interpretation.Comment: 15 pages, harvmac, 3 figure

    Primordial magnetic fields induced by cosmological particle creation

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    We study the primordial magnetic field generated by stochastic currents produced by scalar charged particles created at the beginning of the radiation dominated epoch. We find that for the mass range 10^(-6)GeV \leq m \leq 10^2 GeV, a field of sufficient intensity to seed different mechanisms of galactic magnetic field generation, while still consistent with observational and theoretical constraints, is created coherently over a galactic scale.Comment: accepted for publication in Phys. Rev.

    Quantum electromagnetic field in a three dimensional oscillating cavity

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    We compute the photon creation inside a perfectly conducting, three dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.Comment: 11 pages, 1 figur
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