On Almost Interval Preserving Linear Operators

Siberian Mathematical Journal - A lattice homomorphism between quasi-Banach lattices is known to be compact if and only if it is a sum of a series of rank one lattice...     

Homogeneous orthogonally additive polynomials on vector lattices

It is proved that an orthogonally additive order bounded homogeneous polynomial acting between uniformly complete vector lattices admits a representation in the form of the composition of a linear order bounded operator and a special homogeneous polynomial playing the role of a power-law function, which is absent in the vector lattice. This result helps to establish a criterion for the integral representability of an orthogonally additive homogeneous polynomial.     

Sums of Order Bounded Disjointness Preserving Linear Operators

Siberian Mathematical Journal - Necessary and sufficient conditions are found under which the sum of N order bounded disjointness preserving operators is n-disjoint with n and N naturals. It is...     

Convexity conditions for the space of regular operators

Positivity - In this article we study the following natural questions: When is the quasi-Banach lattice of regular linear operators or homogeneous polynomials between quasi-Banach lattices...     

Representation of orthogonally additive polynomials

We prove that each bounded orthogonally additive homogeneous polynomial acting from an Archimedean vector lattice into a separated convex bornological space, under the additional assumption that the bornological space is complete or the vector lattice is uniformly complete, can be represented as the composite of a bounded linear operator and a special homogeneous polynomial which plays the role of the exponentiation absent in the vector lattice. The approach suggested is based on the notions of convex bornology and vector lattice power.     

Regularity of Continuous Multilinear Operators and Homogeneous Polynomials

Mathematical Notes - Regular multilinear operators and regular homogeneous polynomials acting between Banach lattices are automatically continuous, but the converse, in general, is not true. The...     

On Dominated Extension of Linear Operators

Mathematical Notes - An ordered topological vector space has the countable dominated extension property if any linear operator ranging in this space, defined on a subspace of a separable metrizable...     

On compact domination of homogeneous orthogonally additive polynomials

We prove an analog of the Dodds–Fremlin–Wickstead Theorem on compact domination for homogeneous orthogonally additive polynomials in Banach lattices. The proof is based on linearization of the polynomials which was established earlier by the author.