Atoms and associated spectral properties for positive operators on L^p

Fuente: arXiv
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Main Authors: Delmas, Jean-François, Lefki, Kacem, Zitt, Pierre-André
Format: Preprint
Published: 2023
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author Delmas, Jean-François
Lefki, Kacem
Zitt, Pierre-André
author_facet Delmas, Jean-François
Lefki, Kacem
Zitt, Pierre-André
contents Inspired by Schwartz, Jang-Lewis and Victory, who study in particular generalizations of triangularizations of matrices to operators, we shall give for positive operators on Lebesgue spaces equivalent definitions of atoms (maximal irreducible sets). We also characterize positive power compact operators having a unique non-zero atom which appears as a natural generalization of irreducible operators and are also considered in epidemiological models. Using the different characterizations of atoms, we also provide a short proof for the representation of the ascent of a positive power compact operator as the maximal length in the graph of critical atoms.
format Preprint
id arxiv_https___arxiv_org_abs_2310_15616
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Atoms and associated spectral properties for positive operators on L^p
Delmas, Jean-François
Lefki, Kacem
Zitt, Pierre-André
Spectral Theory
Inspired by Schwartz, Jang-Lewis and Victory, who study in particular generalizations of triangularizations of matrices to operators, we shall give for positive operators on Lebesgue spaces equivalent definitions of atoms (maximal irreducible sets). We also characterize positive power compact operators having a unique non-zero atom which appears as a natural generalization of irreducible operators and are also considered in epidemiological models. Using the different characterizations of atoms, we also provide a short proof for the representation of the ascent of a positive power compact operator as the maximal length in the graph of critical atoms.
title Atoms and associated spectral properties for positive operators on L^p
topic Spectral Theory
url https://arxiv.org/abs/2310.15616