Products of Unconditional Bodies

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


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.


Unit Ball Convex Body Short Proof Symmetric Convex Body Smooth Body 
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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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