Lower bounds on \(\| K^ n \|_{1\to \infty}\) for some contractions \(K\) of \(L^ 2 (\mu)\), with applications to Markov operators
type: Item
instance of: scholarly article
title: Lower bounds on \(\| K^ n \|_{1\to \infty}\) for some contractions \(K\) of \(L^ 2 (\mu)\), with applications to Markov operators
zbMATH Open document ID: 0836.47021
DOI: 10.1007/BF01461012
author: Françoise Lust-Piquard
published in: Mathematische Annalen
publication date: 1996-02-25T00:00:00Z
full work available at URL: https://eudml.org/doc/165388
review text: Let \((X, \mu, d)\) be a measured space. Let \(K\) be a selfadjoint contraction on \(L^2 (X, \mu)\), whose kernel \(k(x, y)\) lives on a fixed neighborhood of the diagonal of \(X\times X\). We prove lower bounds on \(|K^n |_{1\to \infty}\), depending on upper bounds on the measure of the balls of \(X\). Applications to Markov operators on groups and graphs are given, as well as a similar result for the heat operator on some Riemannian manifolds with bounded below Ricci curvature.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 58J35
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 840207
zbMATH Keywords: measured space
zbMATH Keywords: selfadjoint contraction
zbMATH Keywords: Markov operators on groups and graphs
zbMATH Keywords: heat operator on some Riemannian manifolds with bounded below Ricci curvature
MaRDI profile type: Publication
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OpenAlex ID: W2025483481
description: scientific article; zbMATH DE number 840207