Compactness of Multiplication Operators on Riesz Bounded Variation Spaces

We prove compactness of the operator MhCg on a subspace of the space of 2π-periodic functions of Riesz bounded variation on [−π, π], for appropriate functions g and h. Here Mh denotes multiplication by h and Cg convolution by g.

Isometric multiplication operators and weighted composition operators of BMOA

Let u be an analytic function in the unit disk $\mathbb{D}$ D and φ be an analytic self-map of $\mathbb{D}$ D . We give characterizations of the symbols u and φ for which the multiplication operator $M_{u}$ M u and the weighted composition operator $M_{u,\varphi }$ M u , φ are isometries of BMOA.

Spectra and ergodic properties of multiplication and convolution operators on the space $${\mathcal S}({\mathbb R})$$

In this paper we investigate the spectra and the ergodic properties of the multiplication operators and the convolution operators acting on the Schwartz space $${\mathcal S}({\mathbb R})$$ S ( R ) of rapidly decreasing functions, i.e., operators of the form $$M_h: {\mathcal S}({\mathbb R})\rightarrow {\mathcal S}({\mathbb R})$$ M h : S ( R ) → S ( R ) , $$f \mapsto h f $$ f ↦ h f , and $$C_T:{\mathcal S}({\mathbb R})\rightarrow {\mathcal S}({\mathbb R})$$ C T : S ( R ) → S ( R ) , $$f\mapsto T\star f$$ f ↦ T ⋆ f . Precisely, we determine their spectra and characterize when those operators are power bounded and mean ergodic.

Certain Classes of Operators on Some Weighted Hyperbolic Function Spaces

In this paper, some classes of concerned multiplication operators consisting of analytic and hyperbolic functions are defined and considered. Furthermore, some properties such as boundedness and compactness of the new operators are discussed. Finally, a general class of weighted hyperbolic Bloch functions is characterized by metric spaces.