解析函数空间上的自伴加权复合算子

通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。     

Spectra and essential spectral radii of composition operators on weighted Banach spaces of analytic functions

We determine the spectra of composition operators acting on weighted Banach spaces of analytic functions on the unit disc defined for a radial weight v, when the symbol of the operator has a fixed point in the open unit disc. We also investigate in this case the growth rate of the Koenigs eigenfunction and its relation with the essential spectral radius of the composition operator.     

Compact composition operators on weighted Hilbert spaces of analytic functions

We characterize the compactness of composition operators acting on a large family of Hilbert spaces of analytic functions which lie between Bergman and Dirichlet spaces. Our characterization is given in terms of generalized Nevanlinna counting functions.     

Spectra of weighted composition operators on weighted banach spaces of analytic functions

We determine the spectra of weighted composition operators acting on the weighted Banach spaces of analytic functionsH _{ν p} ^∞ when the symbolφ has a fixed point in the open unit disk. Further, we apply this result to give the spectra of composition operators on Bloch type spaces. In particular, we answer in the affirmative a conjecture by MacCluer and Saxe. The research of the second author was partially supported by the Academy of Finland Project No. 51906; the research of this paper was carried out while this author was visiting Kent State University, whose hospitality is acknowledged with thanks.     

Fredholm composition operators on algebras of analytic functions on Banach spaces

We prove that Fredholm composition operators acting on the uniform algebra H^∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.     

Weighted composition operators between weighted spaces of vector-valued holomorphic functions on Banach spaces

Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let U_X and U_Y be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on U_X and U_Y, respectively. Let HV(U_X, E) (or HV₀(U_X, E)) and HW(U_Y, F) (or HW₀(U_Y, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings ? : U_Y → U_X and ψ : U_Y → B(E, F) which generate weighted composition operators between these weighted spaces.     

Superposition operators between weighted Banach spaces of analytic functions of controlled growth

We characterize the entire functions which transform a weighted Banach space of holomorphic functions on the disc of type $H^{\infty }$ into another such space by superposition. We also show that all the superposition operators induced by such entire functions map bounded sets into bounded sets and are continuous. Superposition operators that map bounded sets into relatively compact sets are also considered.     

Spectra of weighted composition operators on algebras of analytic functions on banach spaces

Let E be a complex Banach space, with the unit ball B _E . We study the spectrum of a bounded weighted composition operator u C _φ on H ^∞(B _E ) determined by an analytic symbol φ with a fixed point in B _E such that φ(B _E ) is a relatively compact subset of E, where u is an analytic function on B _E .     

Norm-attaining composition operators on the Bloch spaces

We prove that every composition operator C? on the Bloch space (modulo constant functions) attains its norm and characterize the norm-attaining composition operators on the little Bloch space (modulo constant functions). We also identify the extremal functions for ‖C?‖ in both cases.     

Superposition operators between weighted spaces of analytic functions

Abstract

We study the existence and the continuity of superposition operators between weighted spaces of holomorphic functions in terms of the weights.     

On composition operators on Banach spaces of holomorphic functions

We discuss some spectral properties of composition operators in Banach spaces of holomorphic functions over infinite-dimensional domains. Our results generalize known properties of such operators in the finite-dimensional case.     

Adjoints of composition operators on Hilbert spaces of analytic functions

We observe that a formula for the adjoint of a composition operator, known only for special symbols in some spaces of analytic functions, actually holds for every admissible symbol and in any Hilbert space of analytic functions with reproducing kernels. Along with some new results, all known formulas for the adjoint obtained so far follow easily as a consequence, some in an improved form.     

Weakly compact weighted composition operators on spaces of Lipschitz functions

We prove that if X is a compact metric space and \({\text {lip}}(X,d)\) has the uniform separation property, then weakly compact weighted composition operators on spaces of Lipschitz functions \({\text {Lip}}(X,d)\) and \({\text {lip}}(X,d)\) are compact.     

On the norm and the essential norm of weighted composition operators acting on the weighted Banach space of analytic functions

The objective of this paper is to use known properties of the associated weight to give new estimations of the norm and essential norm of the weighted com- position operators acting between weighted Banach spaces of analytic functions, in terms of composition with certain special functions in these spaces. As a consequence of our results, we obtain genuine extensions of a large number of recent results, and in particular, we extend classical results due to Montes-Rodríguez and Contreras and Hernández-Díaz.     

A note about Volterra operators on weighted Banach spaces of entire functions

We characterize boundedness, compactness and weak compactness of Volterra operators acting between different weighted Banach spaces of entire functions with sup‐norms in terms of the symbol g; thus we complement recent work by Bassallote, Contreras, Hernández‐Mancera, Martín and Paul 3 for spaces of holomorphic functions on the disc and by Constantin and Peláez 16 for reflexive weighted Fock spaces.     

Compact and weakly compact weighted composition operators on weighted spaces of continuous functions

In this note we characterize the compact and weakly compact weighted composition operatorsW _, on certain weighted locally convex spacesCV _o(X, E) of vector-valued continuous functions induced by self maps ofX and the operator-valued mappings XB(E).The work of this author was supported in part by CSIR Grant 9/100/92-EMR-IThe work of this author was supported in part by UGC Grant F.8-7/91 (RBB-II)     

Weighted composition operators on nonlocally convex weighted spaces of continuous functions

LetV be a system of weights on a completely regular Hausdorff spaceX and letB(E) be the topological vector space of all continuous linear operators on a general topological vector spaceE. LetCV ₀(X, E) andCV _b (X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operatorsW _π,? onCV ₀(X, E) (orCV _b (X, E)) induced by the operator-valued mappings π:X→B(E) (or the vector-valued mappings π:X→E, whereE is a topological algebra) and the self-map ? ofX. Also, we characterize the mappings π:X→B(E) (or π:x→E) and ?:X→X which induce the compact weighted composition operators on these weighted spaces of continuous functions.     

Invertible weighted composition operators on weighted function spaces

В статье дается харак теризация обратимых весовых операторов композиц ии, определенных на весо вых локально выпуклы х пространствах непре рывных функций и на весовых п ространствах сечени й, задаваемых семейств ом полунорм, являющихся весовыми аналогами равномерн ой нормы.