In the framework of BIBO stability tests for one-dimensional (1-D) linear systems, the Schur-Cohn stability test has the appealing property of being a recursive algorithm. This is a consequence of the simultaneously algebric and analytic aspect of the Schur coefficients, which can be also regarded as reflection coefficients. In the multidimensional setting, this dual aspect gives rise to two ex...

We prove some general results on sequential convergence in Frechet lattices that yield, as particular instances, the following regarding a closed ideal \(I\) of Banach lattice \(E\): (i) If two \(E\), and \(E/I\) have positive Schur property (the property, respectively) then third has well; (ii) dual \(E\) also this property; (iii) weak Dunford-Pettis property. Examples applications are provided.

A separable Banach space X contains l1 isomorphically if and only if X has a bounded fundamental total wc∗0-stable biorthogonal system. The dual of a separable Banach space X fails the Schur property if and only if X has a bounded fundamental total wc∗0-biorthogonal system.

The double Schur functions form a distinguished basis of the ring Λ(x ||a) which is a multiparameter generalization of the ring of symmetric functions Λ(x). The canonical comultiplication on Λ(x) is extended to Λ(x ||a) in a natural way so that the double power sums symmetric functions are primitive elements. We calculate the dual Littlewood–Richardson coefficients in two different ways thus pr...

We show that, in some cases, the projective and the injective tensor products of two Banach spaces do not have the Dunford-Pettis property (DPP). As a consequence, we obtain that (c0⊗̂πc0)∗∗ fails the DPP. Since (c0⊗̂πc0)∗ does enjoy it, this provides a new space with the DPP whose dual fails to have it. We also prove that, if E and F are L1-spaces, then E⊗̂ǫF has the DPP if and only if both E and...

We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.

The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type A by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood combinatorially from the multiplication in the space of dual k-Schur functions. Using earlier work by the second author, we encode both problems by means of quasisymmetric functions. On the Schubert vs...

By the properties of Schur-convex function, Schur geometrically convex function and Schur harmonically convex function, Schur-convexity, Schur geometric and Schur harmonic convexities of the dual form for a class of symmetric functions are simply proved. As an application, several inequalities are obtained, some of which extend the known ones. Mathematics subject classification (2010): 26D15, 0...

A classic result of I. Schur [9] asserts that for every r 2 and for n sufficiently large, if the set [n]=[1, 2, ..., n] is partitioned into r classes, then at least one of the classes contains a solution to the equation x+ y=z. Any such solution with x{y will be called a Schur triple. Let us say that A [n] has the Schur property if for every partition (or 2-coloring) of A=R _ B (for red and blu...