Let \(X\) be a Banach lattice. Necessary and sufficient conditions for a linear operator \(A:D(A) \to X\), \(D(A)\subseteq X\), to be of positive \(C^0\)-scalar type are given. In addition, the question is discussed which conditions on the Banach lattice imply that every operator of positive \(C^0\)-scalar type is necessarily of positive scalar type
AbstractNatural conditions are imposed on spectra of products and sums of operators. This results in...
The purpose of this paper is to give two characterizations of scalar-type spectral operators
AbstractWe show that a Banach lattice X is r-convex, 1<r<∞, if and only if all positive operators T ...
\(C^0\)-scalar-type spectrality criterions for operators \(A\), whose resolvent set contains the neg...
During the last twenty-five years, the development of the theory of Banach lattices has stimulated n...
We address the question of which functions are positive on all positive operators on Banach lattices...
AbstractWe give several characterizations of Banach lattices on which each positive Dunford–Pettis o...
Abstract. If S, T, R, and K are non-zero positive operators on a Banach lattice such that S ↔ T ↔ R ...
access article distributed under the Creative Commons Attribution License, which permits unrestricte...
summary:We establish some sufficient conditions under which the subspaces of Dunford-Pettis operator...
AbstractThe main result is that if {Tt : t ≥ 0} is a (C0)-semigroup of scalar-type operators (in Dun...
Abstract. We use the method of minimal vectors to prove that certain classes of positive quasinilpot...
AbstractLet T be an invertible positive operator on a Banach lattice E such that the number 0 belong...
AbstractWe characterize Banach lattices for which each positive Dunford–Pettis operator is M-weakly ...
Abstract. For a positive operator Q on a Banach lattice, one defines 〈Q] = {T ≥ 0: TQ ≤ QT} and [Q ...
AbstractNatural conditions are imposed on spectra of products and sums of operators. This results in...
The purpose of this paper is to give two characterizations of scalar-type spectral operators
AbstractWe show that a Banach lattice X is r-convex, 1<r<∞, if and only if all positive operators T ...
\(C^0\)-scalar-type spectrality criterions for operators \(A\), whose resolvent set contains the neg...
During the last twenty-five years, the development of the theory of Banach lattices has stimulated n...
We address the question of which functions are positive on all positive operators on Banach lattices...
AbstractWe give several characterizations of Banach lattices on which each positive Dunford–Pettis o...
Abstract. If S, T, R, and K are non-zero positive operators on a Banach lattice such that S ↔ T ↔ R ...
access article distributed under the Creative Commons Attribution License, which permits unrestricte...
summary:We establish some sufficient conditions under which the subspaces of Dunford-Pettis operator...
AbstractThe main result is that if {Tt : t ≥ 0} is a (C0)-semigroup of scalar-type operators (in Dun...
Abstract. We use the method of minimal vectors to prove that certain classes of positive quasinilpot...
AbstractLet T be an invertible positive operator on a Banach lattice E such that the number 0 belong...
AbstractWe characterize Banach lattices for which each positive Dunford–Pettis operator is M-weakly ...
Abstract. For a positive operator Q on a Banach lattice, one defines 〈Q] = {T ≥ 0: TQ ≤ QT} and [Q ...
AbstractNatural conditions are imposed on spectra of products and sums of operators. This results in...
The purpose of this paper is to give two characterizations of scalar-type spectral operators
AbstractWe show that a Banach lattice X is r-convex, 1<r<∞, if and only if all positive operators T ...