We prove tight bounds for the ∞-norm of the inverse of symmetric diagonally dominant positive matrices. Applications include numerical stability for linear systems, bounds on inverses of differentiable functions, and the consistency of maximum entropy graph distributions from single samples.

We establish weak convergence of the Ishikawa iterates of nonexpansive maps under a variety of new control conditions and without employing any of the properties: (i) Opial’s property (ii) Fréchet differentiable norm (iii) Kadec-Klee property.

We show that if K is a compact metric space then C(K) is a 2-absolute Lipschitz retract. We then study the best Lipschitz extension constants for maps into C(K) from a given metric space M , extending recent results of Lancien and Randrianantoanina. They showed that a finitedimensional normed space which is polyhedral has the isometric extension property for C(K)-spaces; here we show that the s...

We prove that if Y is a closed subspace of a Banach space X such that Y and X/Y admit an equivalent asymptotically uniformly smooth norm, then X also admits an equivalent asymptotically uniformly smooth norm. The proof is based on the use of the Szlenk index and yields a few other applications to renorming theory.

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal.

In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregman’s row action D-projection method fo...

in this article we consider the sequences of sample and population covariance operators for a sequence of arrays of hilbertian random elements. then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

is a vector version of p-Laplacian operator. In order to say what we understand by solution for the problem (1.1), (1.2) we remind some basic results concerning the W 1,p T -spaces. Let C T be the space of indefinitely differentiable T -periodic functions from R to R . We denote by 〈·, ·〉 the inner product on R and by ‖ · ‖, the norm generated by this inner product (the same meaning is applied ...