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

Daniel Berend

doi:10.1090/S0002-9939-1992-1057949-4

A note on the L^p analogue of the “zero-two” law

Daniel Berend

Department of Computer Science

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

2 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	95-97
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	114
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1992-1057949-4
State	Published - 1 Jan 1992

Keywords

Linear contraction
Positive contraction
“Zero-two” law

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9939-1992-1057949-4

Cite this

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AB - 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.

KW - Linear contraction

KW - Positive contraction

KW - “Zero-two” law

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