50,040 research outputs found

    The Dunford-Pettis property on tensor products

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    We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that (c0⊗^πc0)∗∗(c_0\hat{\otimes}_\pi c_0)^{**} fails the DPP. Since (c0⊗^πc0)∗(c_0\hat{\otimes}_\pi c_0)^{*} does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if EE and FF are L1{\mathscr L}_1-spaces, then E⊗^Ï”FE\hat{\otimes}_\epsilon F has the DPP if and only if both EE and FF have the Schur property. Other results and examples are given.Comment: 9 page

    Factorization of weakly continuous holomorphic mappings

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    We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly continuous on weakly bounded sets if and only if it is weakly {\it uniformly\/} continuous on weakly bounded sets. This result was obtained in 1983 by Aron, Herv\'es and Valdivia for polynomials between Banach spaces, and it also holds if the weak topology is replaced by a coarser one. However, we show that it need not be true for a stronger topology, thus answering a question raised by Aron. As an application of the first result, we prove that a holomorphic mapping ff between complex Banach spaces is weakly uniformly continuous on bounded subsets if and only if it admits a factorization of the form f=g∘Sf=g\circ S, where SS is a compact operator and gg a holomorphic mapping

    Modification of the Equivalent Photon Approximation for Resolved Photon Processes

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    We propose a modification of the equivalent photon approximation (EPA) for processes which involve the parton content of the photon, to take into account the suppression of the photonic parton fluxes due to the virtuality of the photon. We present simple, physically motivated ans\"atze to model this suppression and show that even though the parton content of the electron no longer factorizes into an electron flux function and a photon structure function, it is still possible to express it as a single integral. We also show that for the TRISTAN experiments its effect can be numerically of the same size as that of the NLO corrections. Further, we discuss a possible measurement at HERA, which can provide an experimental handle on the effect we model through our ans\"atze.Comment: 8 pages, LaTeX with equations.sty, 3 figures (not included); to appear in the Proceedings of "Photon95", Sheffield, April 1995. A complete compressed PS file, including figures, is available via anonymous ftp from ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-891.ps.
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