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

Michael Lin

ArticleOriginal scientific text

Title

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

Authors ¹

Affiliations

Department of Mathematics and Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel

Abstract

Let T be a positive power-bounded operator on a Banach lattice. We prove: (i) If

\in f_{n} | | T^{n} (I - T) | | < 2

, then there is a k ≥ 1 such that

lim_{n \to \infty} | | T^{n} (I - T^{k}) | | = 0 . (i i)

lim_{n→∞} ||T^n(I-T)|| = 0

if (and o n l y if)

inf_n ||T^n(I-T)|| < √3!$!.

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Title

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

Affiliations

Abstract

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