Continuing the research on the Banach-Saks and Schur properties started in (cf. [10]) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C∗-modules. Some properties of weak module topologies on Hilbert C∗-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studi...

In this paper, we develop a linear programming approach to the synthesis of stabilizing fixed structure controllers for a class of linear time invariant discretetime systems. The stabilization of this class of systems requires the determination of a real controller parameter vector (or simply, a controller), K, so that a family of real polynomials, affine in the parameters of the controllers, i...

We consider the class of doubly diagonally dominant matrices (A = [ ajj] E C”, ‘, la,,1 l”jjl > Ck+ i laiklCk+ jlajkl. i #j) and its subclasses. We give necessary and sufficient conditions in terms of the directed graph for an irreducibly doubly diagonally dominant matrix to be a singular matrix or to be an H-matrix. As in the case of diagonal dominance, we show that the Schur complements of do...

We describe random generation algorithms for a large class of random combinatorial objects called Schur processes, which are sequences of random (integer) partitions subject to certain interlacing conditions. This class contains several fundamental combinatorial objects as special cases, such as plane partitions, tilings of Aztec diamonds, pyramid partitions and more generally steep domino tili...

We present a generalization of the classical Schur modules of GL(N) exhibiting the same interplay among algebra, geometry, and combinatorics. A generalized Young diagram D is an arbitrary finite subset of N × N. For each D, we define the Schur module SD of GL(N). We introduce a projective variety FD and a line bundle LD, and describe the Schur module in terms of sections of LD. For diagrams wit...