The uniform zero-two law for positive operators in Banach lattices

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5 Scopus citations

Abstract

Let T be a positive power-bounded operator on a Banach lattice. We prove: (i) If infn ∥Tn(I - T)∥ < 2, then there is a k ≥ 1 such that limn→∞ ∥Tn(I - Tk)∥ = 0. (ii) limn→∞ ∥Tn(I - T)∥ = 0 if (and only if) infn ∥Tn(I - T)∥ < √3.

Original languageEnglish
Pages (from-to)149-153
Number of pages5
JournalStudia Mathematica
Volume131
Issue number2
DOIs
StatePublished - 1 Jan 1998

ASJC Scopus subject areas

  • Mathematics (all)

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