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

9 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

Access to Document

10.4064/sm-131-2-149-153

Cite this

@article{beb0fc4d08ce43a7976c5c7b8c4adf4c,

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.",

author = "Michael Lin",

year = "1998",

month = jan,

day = "1",

doi = "10.4064/sm-131-2-149-153",

language = "English",

volume = "131",

pages = "149--153",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Institute of Mathematics. Polish Academy of Sciences",

number = "2",

}

TY - JOUR

T1 - The uniform zero-two law for positive operators in Banach lattices

AU - Lin, Michael

PY - 1998/1/1

Y1 - 1998/1/1

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/0040689089

U2 - 10.4064/sm-131-2-149-153

DO - 10.4064/sm-131-2-149-153

M3 - Article

AN - SCOPUS:0040689089

SN - 0039-3223

VL - 131

SP - 149

EP - 153

JO - Studia Mathematica

JF - Studia Mathematica

IS - 2

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this