We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Let L be an Archimedean Riesz space with a weak order unit u. A sufficient condition under which Dedekind [σ-]completeness of the principal ideal Au can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C(X)-spaces. Similar results are obtained for the Riesz spaces Bn(T ), n = 1, 2, . . . , of all functions o...

Riesz potentials and Laplacian of fractal measures in metric spaces are introduced. They deene self{adjoint operators in the Hilbert space L 2 () and the former are shown to be compact. In the euclidean case the corresponding spectral asymptotics are derived by Besov space methods. The inverses of the Riesz potentials are fractal pseudo-diierential operators. For the Laplace operator the spectr...

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

In this paper, we investigate duality of modular g-Riesz bases and g-Riesz bases in Hilbert C*-modules. First we give some characterization of g-Riesz bases in Hilbert C*-modules, by using properties of operator theory. Next, we characterize the duals of a given g-Riesz basis in Hilbert C*-module. In addition, we obtain sufficient and necessary condition for a dual of a g-Riesz basis to be agai...

In this paper, we consider a Riesz space-fractional reaction-dispersion equation (RSFRDE). The RSFRDE is obtained from the classical reaction-dispersion equation by replacing the second-order space derivative with a Riesz derivative of order β ∈ (1,2]. We propose an implicit finite difference approximation for RSFRDE. The stability and convergence of the finite difference approximations are ana...

1971 The purpose of this paper is to exhibit a theory of integration which can be used on a large class of topological spaces and which generalizes the theory of integration over the locally compact Hausdorff spaces. The first part of the paper is devoted to the construction of such a theory. An integral is viewed as a positive linear functional having a certain extension property on a particul...

Various equivalent conditions under which a frame is a Riesz basis of a separable Hilbert space are known. See [8] among others, for instance. We add two new conditions to the list. They are inspired by the projection method proposed in [2], which approximates frame coefficients by using finite subsets of a frame. Our main approach is to transcribe anything involving a frame in a Hilbert space ...

We give a sufficient condition for a univalently induced composition operator on the Hardy space H2 to be a Riesz operator. We then establish that every Riesz composition operator has a Koenigs model and explore connections our work has with the model theory and spectral theory of composition operators.

Let G be a countable group of unitary operators on a complex separable Hilbert space H. We give a characterization of biorthogonality among Riesz multiwavelets in terms of certain invariant properties of their associated core spaces. A large family of non-biorthogonal Riesz multiwavelets is exhibited. We also discuss some results on linear perturbation of orthonormal multiwavelets.