An interpolation result for the spectral radius
type: Item
instance of: scholarly article
title: An interpolation result for the spectral radius
zbMATH Open document ID: 0657.47042
DOI: 10.1007/BF01164016
author: Peter Meyer-Nieberg
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173745
review text: Let be E a Banach lattice with order continuous norm and T a positive linear operator on E. Let EX(T) denote the family of all Banach lattices F, which contain a norm dense ideal \(F_ 0\) isomorphic to an order dense T-invariant ideal of E and satisfying \(\| T| F_ 0\|_ F<\infty\). In the main theorem of the paper it is proved that if \(F\in EX(T)\) and \[ \text{spectral radius}(T:F\to F)\leq \lambda \leq \text{spectral radius }(T:E\to E) \] then there exists a canonical \(H(\lambda)\in EX(T)\) with \[ \text{spectral radius}(T:H(\lambda)\to H(\lambda))=\lambda. \]
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 4073802
zbMATH Keywords: Banach lattice with order continuous norm
zbMATH Keywords: positive linear operator
reviewed by: László Zsidó
MaRDI profile type: Publication
cites work: Q5539994
cites work: Interpolation of spectral operators
cites work: On the spectra of linked operators
cites work: Q3708589
cites work: A partial spectral reduction for positive linear operators
cites work: Q4049667
cites work: Interpolation of spectra
description: scientific article; zbMATH DE number 4073802