Let ∆ be an infinite, locally finite tree with more than two ends. Let Γ < Aut(∆) be an acylindrical uniform lattice. Then the boundary algebra AΓ = C(∂∆) Γ is a simple Cuntz-Krieger algebra whose K-theory is determined explicitly.

We prove a quantized version of a theorem by M. V. Shĕınberg: A uniform algebra equipped with its canonical, i.e. minimal, operator space structure is operator amenable if and only if it is a commutative C∗-algebra.

A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new construction of the Berkovich analytic space associated to an affinoid algebra as the completion of a canonical uniform structure on the associated rigid-an...

Following ideas of A. C. Cochran, we give a suitable definition of a saturated uniformly A-convex algebra. In the m-convex case, such algebra is a uniform topological one.

We consider two different notions of convexity of metric spaces, namely (strict/uniform) ball convexity and (strict/uniform) distance convexity. Our main theorem states that (strict/uniform) distance convexity is preserved under a fairly general product construction, whereas we provide an example which shows that the same does not hold for (strict/uniform) ball convexity, not even when consider...

We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of PérezGarćıa for the trace class, this completes the answer to a long-standing question of Varopoulos.

In this paper several results of N. Noble concerning closed projections are extended using generalizations of first countable, Frechet, and sequential spaces. We also consider compactness conditions defined by requiring that certain nets have cluster points.

In this paper, we studied the long-time properties of solutions generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for nonlinear source term g (u) and Kirchhoff stress term M (s) in equation, existence uniqueness solution proved by using uniform prior estimates time Galerkin’s finite element method. Then, abounded absorption set B0k is obta...