Irreducible compact operators
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.
positive, compact, ideal-irreducible operator in a Banach lattice
positive irreducible operators, some powers of which majorizes a compact positive operator
scientific article; zbMATH DE number 3981881
scientific article