Irreducible compact operators
type: Item
instance of: scholarly article
title: Irreducible compact operators
zbMATH Open document ID: 0607.47033
DOI: 10.1007/BF01162028
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173723
review text: The author proves the following nice result. Let T be a positive, compact, ideal-irreducible operator in a Banach lattice E (dim \(E\geq 2)\). Then T is not quasi-nilpotent, i.e. \(r(T)>0\) where, of course, r(T) denotes the spectral radius) of T. There is also a generalization of this result to positive irreducible operators, some powers of which majorizes a compact positive operator. This class of operators was considered by \textit{V. Caselles} [Indagationes Math. 48, 11-16 (1986; Zbl 0595.47030)]. For still another generalization see the next review.
Mathematics Subject Classification ID: 47B60
Mathematics Subject Classification ID: 47B06
Mathematics Subject Classification ID: 46B42
zbMATH DE Number: 3981881
zbMATH Keywords: positive, compact, ideal-irreducible operator in a Banach lattice
zbMATH Keywords: not quasi-nilpotent
zbMATH Keywords: spectral radius
zbMATH Keywords: positive irreducible operators, some powers of which majorizes a compact positive operator
author: B. de Pagter
reviewed by: Y. A. Abramovich
MaRDI profile type: Publication
cites work: A characterization of weakly sequentially complete Banach lattices
cites work: Compact operators in Banach lattices
cites work: Q5638775
cites work: Hilden's simple proof of Lomonosov's invariant subspace theorem
cites work: Topologische Nilpotenz irreduzibler Operatoren
cites work: Q4049667
cites work: Q3669960
OpenAlex ID: W2054977546
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description: scientific article; zbMATH DE number 3981881