A note on the Lp analogue of the “zero-two” law

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T was proved by R. Wittmann [2] that, given a positive linear contraction of Lp (1 ≤ p ≤ ∞), sup∥f∥≤1 limn⟶∞∥Tn f − Tn+1 f∥ is either ≥ αp or 0; the (best possible) value of αp is the lp-norm of a certain 3×3 matrix. In this paper αp is explicitly expressed as a function of p.

Original languageEnglish
Pages (from-to)95-97
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number1
StatePublished - 1 Jan 1992


  • Linear contraction
  • Positive contraction
  • “Zero-two” law

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics


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