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

Michael Lin

doi:10.4064/sm-131-2-149-153

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

Michael Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	149-153
Number of pages	5
Journal	Studia Mathematica
Volume	131
Issue number	2
DOIs	https://doi.org/10.4064/sm-131-2-149-153
State	Published - 1 Jan 1998

ASJC Scopus subject areas

General Mathematics

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title = "The uniform zero-two law for positive operators in Banach lattices",

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.",

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AB - 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.

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

Abstract

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