Composition Operators between Weighted Banach Spaces of Analytic Functions
نویسندگان
چکیده
We characterize those analytic self-maps <p of the unit disc which generate bounded or compact composition operators Cv between given weighted Banach spaces H£° or H® of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v. 1991 Mathematics subject classification (Amer. Math. Soc): primary 47B38; secondary 3OD55, 46E15.
منابع مشابه
Essential norm estimates of generalized weighted composition operators into weighted type spaces
Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...
متن کاملGeneralized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...
متن کاملComposition operators acting on weighted Hilbert spaces of analytic functions
In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators are investigated.
متن کاملNorm-attaining weighted composition operators on weighted Banach spaces of analytic functions
We investigate weighted composition operators that attain their norm on weighted Banach spaces of holomorphic functions on the unit disc of type H∞. Applications for composition operators on weighted Bloch spaces are given.
متن کاملWeighted composition operators between growth spaces on circular and strictly convex domain
Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...
متن کامل