let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

On Operators whose Compactness Properties are defined by Order by Safak Alpay Abstract. Let E be a Banach lattice. A subset B of E is called order bounded if there exist a, b in E such that a ≤ x ≤ b for each x ∈ B. Considering E in E′′, the bidual of E, a subset B of E is called b-order bounded in E if it is order bounded in the Banach lattice E′′. A bounded linear operator T : E → X is called...

The present paper proposes a fast numerical method for the linear Volterra integral equations withregular and weakly singular kernels having smooth solutions. This method is based on the approx-imation of the kernel, to simplify the integral operator and then discretization of the simpliedoperator using a forward dierence formula. To analyze and verify the accuracy of the method, weexamine samp...

In this paper, we introduce and study new concepts of order L-weakly M-weakly compact operators. As consequences, obtain some characterizations Banach lattices with continuous norms or whose topological duals have norms. It is proved that if $$T:E \longrightarrow F$$ an operator between two lattices, then T only its adjoint $$T'$$ compact. Also, show compact, Some related results are also obtai...

In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

We show that if X is a L∞-space with the Dieudonnè property and Y is a Banach space not containing l1, then any operator T : X⊗ Y → Z, where Z is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained. Let X be a L∞-space (see [1] for this notion and some useful results on L∞-spaces) and Y be a Banach space not containing l1.We consider ...

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to bounded linear operator $\widehat {f} \mathcal {F}(M) {F}(N)$ their corresponding Lipschitz-free spaces. In this paper, we give necessary and sufficient condition for {f}$ compact terms of conditions on $f$ . This extends result by A. Jiménez-Vargas M. Villegas-Vallecillos the case non-separable...

We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces. §

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...