Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. The product trapezoidal method is applied for discretization of the integral term. The order of accuracy in space and time is , where . Stability and convergence in  norm are discussed through energy method. Numerical examples are provided to confirm the theoretical prediction ...

we investigate the problem of the existence of a frame forright ideals of a C*-algebra A, without the use of the Kasparov stabilizationtheorem. We show that this property can not characterize A as a C*-algebraof compact operators.

We investigate compact composition operators on ceratin Lipschitzspaces of analytic functions on the closed unit disc of the plane.Our approach also leads to some results about compositionoperators on Zygmund type spaces.

In this paper we consider a mixed boundary value problem with nonhomogeneous, nonlinear differential operator (called double phase operator), convection term (a reaction depending on the gradient), three multivalued terms, and an implicit obstacle constraint. Under very general assumptions data, prove that solution set of such is nonempty (so there at least one solution) weakly compact. The pro...

For an R-bounded families of operators on L1 we associate a family of representing measures and show that they form a weakly compact set. We consider a sectorial operator A which generates an R-bounded semigroup on L1. We show that given 2 > 0 there is an invertible operator U : L1 → L1 with ‖U − I‖ < 2 such that for some positive Borel function w we have U(D(A)) ⊃ L1(w).

The purpose of this paper is to introduce and study the notion of a vector-valued π-invariant mean associated to a unitary representation π of a locally compact groupG on S, a self-adjoint linear subspace containing I of B(Hπ). We obtain, among other results, an extension theorem for π-invariant completely positive maps and π-invariant means which characterizes amenability of G. We also study v...

For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

Recently, continuous functionals for unbounded order (norm, weak and weak*) in Banach lattices were studied. In this paper, we study the operators with respect to convergences. We first investigate approximation property of convergence. Then show some characterizations continuity uo, un, uaw uaw*-convergence. Based on these results, discuss order-weakly compact lattices.