m at h . FA ] 2 5 A pr 1 99 4 When every polynomial is
نویسنده
چکیده
Letting E, F be Banach spaces, the main two results of this paper are the following: (1) If every (linear bounded) operator E → F is unconditionally converging, then every polynomial from E to F is unconditionally converging (definition as in the linear case). (2) If E has the Dunford-Pettis property and every operator E → F is weakly compact, then every k-linear mapping from E into F takes weak Cauchy sequences into norm convergent sequences. In particular, every polynomial from l∞ into a space containing no copy of l∞ is completely continuous. This solves a problem raised by the authors in a previous paper, where they showed that there exist nonweakly compact polynomials from l∞ into any nonreflexive space.
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تاریخ انتشار 1994