arXiv subjects
Publications and source records attributed to Julio C. Ramos Fernández.
We make an exhaustive study of the properties of multiplication operator $M_u$ acting on Köthe spaces. We characterize the multiplication operators, acting on Köthe spaces, which are: bounded, injective, onto, bijective, Fredholm, compact, with closed range and with range finite. We also study the spectrum, the $n$-power and calculate the essential norm of $M_u$ and we study the algebra of multiplication operators.
For an almost radial and typical weight $v$, we characterize the continuity and compactness of the weighted composition operator $u C_φ$ acting on the weighted Banach spaces of analytic functions $H_{v}^{\infty}$ in terms of the $n$th power of the symbol $φ$, where $u: \mathbb{D} \to \mathbb{C}$ is an analytic function and $φ: \mathbb{D} \to \mathbb{D}$ is analytic. More precisely, we extend the results of Hyvärinen, Kemppainen, Lindström, Rautio and Saukko relating to the continuity and essential norm calculus of the operator $u C_φ$.