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Products of Unconditional Bodies

  • Béla Bollobás
  • Imre Leader
Conference paper
Part of the Operator Theory Advances and Applications book series (OT, volume 77)

Abstract

In this paper, we consider products K · L of unconditional bodies in ℝn. For an unconditional body M in ℝ n , we introduce the notion of the M-dual Ko M of an unconditional body K: the maximal body L such that K · L ⊂ M; thus the l n 1-dual is the usual dual. We prove that if M is the unit ball of l n p , 1 ≤ p ≤ ∞, and K and L are unconditional bodies that are maximal subject to K · LM, then K ·L = M; in other words, for any K we have \( K_M^{oo} \cdot K_M^o = M \) · K M O = M. This generalises Lozanovskii’s theorem. We also construct an example to show that equality need not hold for a general unconditional body M: \( M:\;K_M^{oo} \cdot K_M^o = M \) · K M O = M does not hold in general.

Keywords

Unit Ball Convex Body Short Proof Symmetric Convex Body Smooth Body 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 1995

Authors and Affiliations

  • Béla Bollobás
    • 1
  • Imre Leader
    • 1
  1. 1.Department of Pure Mathematics and Mathematical StatisticsCambridge UniversityCambridgeEngland

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