ACTA UNIVERSITATIS APULENSIS No 18/2009 MULTIPLICATION OPERATORS ON NON-LOCALLY CONVEX WEIGHTED FUNCTION SPACES
نویسندگان
چکیده
Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping and f ∈ F , let Mπ(f)(x) := π(x)f(x). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be a multiplication operator on F (i.e. a continuous self-mapping on F) in the non-locally convex setting. These results unify and improve several known results. 2000 Mathematics Subject Classification: 47B38, 46E40, 46A16
منابع مشابه
ACTA UNIVERSITATIS APULENSIS No 19/2009 ON PRECOMPACT MULTIPLICATION OPERATORS ON WEIGHTED FUNCTION SPACES
Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary a...
متن کاملACTA UNIVERSITATIS APULENSIS No 19/2009 ON CLOSE-TO-CONVEX FOR CERTAIN INTEGRAL OPERATORS
In this paper, we consider some sufficient conditions for two integral operators to be close-to-convex function defined in the open unit disk.
متن کاملACTA UNIVERSITATIS APULENSIS No 20/2009 UNIFORMLY STARLIKE AND CONVEX UNIVALENT FUNCTIONS BY USING CERTAIN INTEGRAL OPERATORS
An extension of k-uniformly starlike and convex functions are introduced by making use of an integral operator. Inclusion relations and coefficient bounds for these classes are determined and consequently, some known results are generalized. 2000 Mathematics Subject Classification: Primary 30C45; Secondary 30C50.
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 کاملACTA UNIVERSITATIS APULENSIS No 17/2009 ABOUT SOME BIVARIATE OPERATORS OF STANCU TYPE
In this paper, we will obtain a form of Bernstein-Stancu bivariate operators and finally we will give an approximation theorem for them. 2000 Mathematics Subject Classification: 41A10, 41A25, 41A36, 41A63.
متن کامل