On planarity of compact, locally connected, metric spaces

On a Metric on Translation Invariant Spaces

In this paper we de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

Shift Invariant Spaces and Shift Preserving Operators on Locally Compact Abelian Groups

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

The Role of Connectedness in the Structure and the Action of Group of Isometries of Locally Compact Metric Spaces

By proving that, if the quotient space Σ(X) of the connected components of the locally compact metric space (X, d) is compact, then the full group I(X, d) of isometries of X is closed in C(X, X) with respect to the pointwise convergence topology, i.e., that I(X, d) coincides in this case with its Ellis’ semigroup, we complete the proof of the following: Theorem (a): If Σ(X) is not compact, I(X,...

On Some Properties of Analytic Spaces Connected with Bergman Metric Ball

Weighted Composition Operators Between Extended Lipschitz Algebras on Compact Metric Spaces

‎In this paper, we provide a complete description of weighted composition operators between extended Lipschitz algebras on compact metric spaces. We give necessary and sufficient conditions for the injectivity and the sujectivity of these operators. We also obtain some sufficient conditions and some necessary conditions for a weighted composition operator between these spaces to be compact.