The Lempert function of the symmetrized polydisc in higher dimensions is not a distance

We prove that the Lempert function of the symmetrized polydisc in dimension greater than two is not a distance.

     

Products of integral-type operators and composition operators between Bloch-type spaces

A complete picture on the boundedness and compactness of the products of integral-type operators and composition operators between Bloch-type spaces of holomorphic functions on the unit disk is given in this paper.     

Compact differences of composition operators

A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component.     

A variational approach to norm attainment of some operators and polynomials

If X is an Asplund space, then every uniformly continuous function on Bx＊ which is holomorphic on the open unit ball, can be perturbed by a w＊ continuous and homogeneous polynomial on X＊ to obtain a norm attaining function on the dual unit ball. This is a consequence of a version of Bourgain-Stegall＇s variational principle. We also show that the set of N-homogeneous polynomials between two Banach spaces X and Y whose transposes attain their norms is dense in the corresponding space of N-homogeneous polynomials. In the case when Y is the space of Radon measures on a compact K, this result can be strengthened.     

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.     

Norms of composition operators with rational symbol

We compute the norms of composition operators with rational symbols that satisfy certain properties, extending Christopher Hammond's methods on operators with linear fractional symbols. This leads to a host of new examples of composition operators whose norms are calculable.     

Adjoints of composition operators with rational symbol

Building on techniques developed by Cowen and Gallardo-Gutiérrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H². We consider some specific examples, comparing our formula with several results that were previously known.     

Hypercyclic property of weighted composition operators

In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.

     

Isometric composition operators on the analytic Besov spaces

We investigate the isometric composition operators on the analytic Besov spaces. For 1<p<2$1<p<2$ we show that an isometric composition operator is induced only by a rotation of the disk. For p>2$p>2$, we extend previous work on the subject. Finally, we analyze this same problem for the Besov spaces with an equivalent norm.     

Adjoints of rationally induced composition operators

We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H² [Christopher Hammond, Jennifer Moorhouse, Marian E. Robbins, Adjoints of composition operators with rational symbol, J. Math. Anal. Appl. 341 (2008) 626-639]. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator.     

On composition operators onH p -spaces in several variables

In this paper, we prove that a composition operator onH ^p (B) is Fredholm if and only if it is invertible if and only if its symbol is an automorphism onB, and give the representation of the spectra of a class of composition operators. In addition, using composition operator, we discuss intertwining Toeplitz operators. Supported by NNSF and PDSF     

Generalized composition operators on Zygmund spaces and Bloch type spaces

The boundedness and compactness of the generalized composition operator on Zygmund spaces and Bloch type spaces are investigated in this paper.     

Composition operators on noncommutative Hardy spaces

In this paper we initiate the study of composition operators on the noncommutative Hardy space , which is the Hilbert space of all free holomorphic functions of the form

     

Topological structures of the sets of composition operators on the Bloch spaces

We study properties of the topological sets of composition operators on Bloch and little Bloch spaces in the operator topology.     

Linear sums of two composition operators on the Fock space

Linear sums of two composition operators of the multi-dimensional Fock space are studied. We show that such an operator is bounded only when both composition operators in the sum are bounded. So, cancelation phenomenon is not possible on the Fock space, in contrast to what have been known on other well-known function spaces over the unit disk. We also show the analogues for compactness and for membership in the Schatten classes. For linear sums of more than two composition operators the investigation is left open.     

On the Toeplitzness of the adjoint of composition operators

Building on techniques developed by Cowen (1988)  [3] and Nazarov–Shapiro (2007)  [10], it is shown that the adjoint of a composition operator, induced by a unit disk-automorphism, is not strongly asymptotically Toeplitz. This result answers Nazarov–Shapiro’s question in Nazarov and Shapiro (2007)  [10].     

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.     

The spectra of composition operators from linear fractional maps acting upon the Dirichlet space

Let φ:D→D be a non-constant linear fractional transformation (necessarily of the form ). Let D denote the Dirichlet space of analytic functions. We determine the spectrum of the composition operator C_?:D→D defined by C_?(f)=f°φ. Eigenfunctions for the operator C_?:H²→H² frequently do not belong to the space D. However, spectral results for the operator C_?:D→D, much like those that have already been demonstrated for the operator C_?:H²→H², are presented in this paper.     

Bergman空间上复合算子的紧性刻划

研究了C^n中有界强拟凸Ω上Bergman空间A^p(Ω)上的复合算子的有界性、紧性，给出了复合算子Cψ：A^p(Ω)→A^p(Ω)紧性的一个完整刻划。     

The Schur algorithm and coefficient characterizations for generalized Schur functions

In this paper we analyze the existence of a Schur algorithm and obtain coefficient characterizations for the functions in a generalized Schur class. An application to an interpolation problem of Carathéodory type raised by M.G. Krein and H. Langer is indicated.