On approximation of copulas.
On extensions of orthosymmetric lattice bimorphisms
In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if is a commutative -algebra and its Dedekind completion, then, can be equipped...
On invariant elements for positive operators.
In the paper we study the existence of nonzero positive invariant elements for positive operators in Riesz spaces. The class of Riesz spaces for which the results are valid is large enough to contain all the Banach lattices with order continuous norms. All the results obtained in earlier works deal with positive operators in KB-spaces and in many of them the approach is based upon the use of Banach limits. The methods created for KB-spaces cannot be extended to our more general setting; that is...
On invariant measures for power bounded positive operators
We give a counterexample showing that does not imply the existence of a strictly positive function u in with Tu = u, where T is a power bounded positive linear operator on of a σ-finite measure space. This settles a conjecture by Brunel, Horowitz, and Lin.
On nonnegative operators and fully cyclic peripheral spectrum.
On peripheral eigenvalues and eigenvectors of certain regular operators. (Über periphere Eigenwerte und Eigenvektoren bei gewissen regulären Operatoren.)
On spectral continuity of positive elements
Let x be a positive element of an ordered Banach algebra. We prove a relationship between the spectra of x and of certain positive elements y for which either xy ≤ yx or yx ≤ xy. Furthermore, we show that the spectral radius is continuous at x, considered as an element of the set of all positive elements y ≥ x such that either xy ≤ yx or yx ≤ xy. We also show that the property ϱ(x + y) ≤ ϱ(x) + ϱ(y) of the spectral radius ϱ can be obtained for positive elements y which satisfy at least one of the...
On stability of classes of Lipschitz mappings generated by compact sets of linear mappings.
On subinvariant measures for positive operators in L1
On the class of b-L-weakly and order M-weakly compact operators
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
On the class of order almost L-weakly compact operators
We introduce a new class of operators that generalizes L-weakly compact operators, which we call order almost L-weakly compact. We give some characterizations of this class and we show that this class of operators satisfies the domination problem.
On the Cohen -nuclear sublinear operators.
On the dependence of the orthogonal projector on deformations of the scalar product
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
On the equality between some classes of operators on Banach lattices
We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.
On the extension of positive linear functionals.
On the orbits of an operator with spectral radius one
On the positivity of semigroups of operators
In a Banach space , let be a -semigroup with generating operator . For a cone ...
On the spectral radius of positive operators.
On the spectral radius of positive operators (Corrigendum).
On the spectrum of orthomorphisms and Barbashin operators.