In this work cylindrical Wiener processes on Banach spaces are defined by means of cylindrical stochastic processes, which are a well considered mathematical object. This approach allows a definition which is a simple straightforward extension of the real-valued situation. We apply this definition to introduce a stochastic integral with respect to cylindrical Wiener processes. Again, this defin...

In this article we define measurable multifunctions in nonseparable Banach spaces, prove a weak compactness criterion for the selectors of multifunctions integrably bounded, characterize Banach spaces that have the Radon–Nikodym property by means of convergence of multivalued martingales, generalize some recent results on convergence of set-valued conditional expectations, and give some applica...

A logarithmic residue is a contour integral of the (left or right) logarithmic derivative of an analytic Banach algebra valued function. Logarithmic residues are intimately related to sums of idempotents. The present paper is concerned with logarithmic residues and sums of idempotents in the Banach algebra generated by the compact operators and the identity in the case when the underlying Banac...

We employ the Borsuk-Krasnoselskii antipodal theorem to prove a new fixed point theorem in ordered Banach spaces. Then, the applicability of the result is shown by presenting sufficient conditions for the existence of solutions to initial value problems for first-order difference equations in Banach spaces. To prove that result we shall employ set valued analysis techniques.

The S–transform is shown to satisfy a specific twisted multiplicativity property for free random variables in a B–valued Banach noncommutative probability space, for an arbitrary unital complex Banach algebra B. Also, a new proof of the additivity of the R–transform in this setting is given.

Abstract. Here a new condition for the geometry of Banach spaces is introduced and the operator–valued Fourier multiplier theorems in weighted Besov spaces are obtained. Particularly, connections between the geometry of Banach spaces and Hörmander-Mikhlin conditions are established. As an application of main results the regularity properties of degenerate elliptic differential operator equation...

In this paper, we introduce complex valued rectangular b-metric spaces. We prove an analogue of Banach contraction principle. We also prove a different contraction principle with a new condition and a fixed point theorem in this space. Finally, we give an application of Banach contraction principle to linear equations. c ©2015 All rights reserved.

A fourth-order accurate embedded boundary method for the scalar wave equation with Dirichlet or Neumann boundary conditions is described. The method is based on a compact Pade-type discretization of spatial derivatives together with a Taylor series method (modified equation) in time. A novel approach for enforcing boundary conditions is introduced which uses interior boundary points instead of ...

We study the complexity of Banach space valued integration. The input data are assumed to be r-smooth. We consider both definite and indefinite integration and analyse the deterministic and the randomized setting. We develop algorithms, estimate their error, and prove lower bounds. In the randomized setting the optimal convergence rate turns out to be related to the geometry of the underlying B...

As is often the case when Fourier series techniques are used, we consider spaces of complex valued functions. Let Lp(S1) denote the Banach space of Lebesgue p-integrable functions and its norm by ‖ · ‖p. In the case of L2(S1), the norm is derived from the hermitian product ∫ 2π 0 f(θ)g(θ)dθ. Let Rθ and fφ denote the extension R of r according to (3.2) and fβ after the reparameterization. Our ta...