This dissertation originates from a classical result that the `-stability of the convolution operator associated with a summable sequence are equivalent to each other for 1 ≤ p ≤ ∞. This dissertation is motivated by the recent result by C. E. Shin and Q. Sun (Journal of Functional Analysis, 256(2009), 2417–2439), where the `-stability of infinite matrices in the Gohberg-Baskakov-Sjöstrand class...

Starting from the study of the Shepard nonlinear operator of maxprod type in [2], [3], in the recent monograph [4], Open Problem 5.5.4, pp. 324-326, the Baskakov max-prod type operator is introduced and the question of the approximation order by this operator is raised. The aim of this note is to obtain the order of uniform approximation Cω1(f ; 1 √ n ) (with the explicit constant C = 24) of an...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...