LW-compact operators and domination problem

Positivity - This paper introduces a ‘new’ class of operators. An operator T from a Banach lattice E into a Banach space Y will be called an LW-compact if T carries L-weakly compact...     

Disjointly improjective operators and domination problem

In this work we introduce the disjointly improjective operators between Banach lattices. We investigate this class of operators. Also, we extend the Flores–Hernández’s theorem on the domination problem by disjoint strictly singular operator.     

On positive strictly singular operators and domination

We study the domination problem by positive strictly singular % operators between Banach lattices. Precisely we show that if E and %F are two Banach lattices such that the norms on E' and F are %order continuous and E satisfies the subsequence splitting property, %and %0S T : E F are two positive operators, then T strictly %singular implies S strictly singular. The special case of %endomorphisms is also considered. Applications to the class of %strictly co-singular (or Pelczynski) operators are given too.     

On the diagonal queens domination problem

It is shown that the problem of covering an n × n chessboard with a minimum number of queens on a major diagonal is related to the number-theoretic function r₃(n), the smallest number of integers in a subset of {1,…,n} which must contain three terms in arithmetic progression.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

On domination problem of non-negative distributions

The domination relationship between non-negative distributions is an important question in applied probability. It has important applications in the fields of finance, insurance and risk theory. In this paper, based on class ℳ, we find the sufficient condition of dominating all light-tailed distributions and also discuss its necessity. Almost all heavy-tailed distributions often used in risk theory satisfy this condition. We also consider the domination problem between heavy-tailed distributions, and show that classes      

Maharam-type kernel representation for operators with a trigonometric domination

Consider a linear and continuous operator T between Banach function spaces. We prove that under certain requirements an integral inequality for T is equivalent to a factorization of T through a specific kernel operator: in other words, the operator T has what we call a Maharam-type kernel representation. In the case that the inequality provides a domination involving trigonometric functions, a special factorization through the Fourier operator is given. We apply this result to study the problem that motivates the paper: the approximation of functions in \(L^{2}[0,1]\) by means of trigonometric series whose Fourier coefficients are given by weighted trigonometric integrals.     

Modelling and solving the perfect edge domination problem

Optimization Letters - A formulation is proposed for the perfect edge domination problem and some exact algorithms based on it are designed and tested. So far, perfect edge domination has been...     

On spectrally associated Schur functions,Arov-inner functions and a Nehari-type completion problem for Schur functions

This paper studies a special Nehari-type completion problem for matrix-valued Schur functions. Several necessary and sufficient conditions for solvability of the problem are given. If a solution exists, then it is unique and it can be expressed explicitly by the original data.     

Generalized strong vector quasi-equilibrium problem with domination structure

In this paper, a generalized strong vector quasi-equilibrium problem with set-valued mapping and domination structure is presented, and under the condition of cone-continuity, existence of solutions and the compactness of solution set are established. As applications, existence of solutions for strong vector F-implicit variational inequality problem and strong vector F-implicit complementarity problem is derived, and Khan’s main results are corrected.     

An extremal problem for edge domination insensitive graphs

A connected graph is edge domination insensitive if the domination number is unchanged when any single edge is removed. The minimum number of edges required by such a graph is determined. Similar results are given when the graph must remain connected upon any edge's removal and when the dominating set must remain fixed.     

Realizations for Schur upper triangular operators centered at an arbitrary point

Reproducing kernel spaces introduced by L. de Branges and J. Rovnyak provide isometric, coisometric and unitary realizations for Schur functions, i.e. for matrix-valued functions analytic and contractive in the open unit disk. In our previous paper [12] we showed that similar realizations exist in the nonstationary setting, i.e. when one considers upper triangular contractions (which appear in time-variant system theory as transfer functions of dissipative systems) rather than Schur functions and diagonal operators rather than complex numbers. We considered in [12] realizations centered at the origin. In the present paper we study realizations of a more general kind, centered at an arbitrary diagonal operator. Analogous realizations (centered at a point of the open unit disk) for Schur functions were introduced and studied in [3] and [4].     

The Schur complement and the inverse M-matrix problem

It is well known that if M is a nonnegative nonsingular inverse M-matrix and if A is a nonsingular block in the upper left hand corner, then the Schur complement of A in M, (M ? A), is an inverse M-matrix. The converse of this is generally false. In this paper we give added restrictions on M or A to insure the converse, and give some necessary and sufficient conditions for HMH^?1, where H = I⊕(?I), to be an M-matrix.     

The matricial Schur problem in both nondegenerate and degenerate cases

The principal object of this paper is to present a new approach simultaneously to both nondegenerate and degenerate cases of the matricial Schur problem. This approach is based on an analysis of the central matrixvalued Schur functions which was started in [24]–[26] and then continued in [27]. In the nondegenerate situation we will see that the parametrization of the solution set obtained here coincides with the well‐known formula of D. Z. Arov and M. G. Kre?n for that case (see [1]). Furthermore, we give some characterizations of the situation that the matricial Schur problem has a unique solution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)