Norms Of Composition Operators Research Articles

Sharp inequalities for holomorphic function spaces

In this paper we establish some sharp inequalities for holomorphic Fock spaces in Cn and weighted Bergman spaces in the unit polydisk, which generalizes some results of Burbea. As an application, we prove Furdui's conjecture about the norm of composition operators between Fock spaces.

Norms of composition operators between Fock spaces

In this paper we give some estimates on norms of bounded composition operators between Fock spaces. In particular, when $$q<p$$ and $$\varphi (z)=Az+B$$ with $$\Vert A\Vert \le 1$$, we determine exactly the norm of the bounded composition operator $$C_{\varphi }: F^p\rightarrow F^q$$.

Norms of composition operators on the H2 space of Dirichlet series

We consider composition operators Cφ on the Hardy space of Dirichlet series H2, generated by Dirichlet series symbols φ. We prove two different subordination principles for such operators. One concerns affine symbols only, and is based on an arithmetical condition on the coefficients of φ. The other concerns general symbols, and is based on a geometrical condition on the boundary values of φ. Both principles are strict, in the sense that they characterize the composition operators of maximal norm generated by symbols having given mapping properties. In particular, we generalize a result of J.H. Shapiro on the norm of composition operators on the classical Hardy space of the unit disc. Based on our techniques, we also improve the recently established upper and lower norm bounds in the special case that φ(s)=c+r2−s. A number of other examples are given.

The norm of composition operators on the Fock space

ABSTRACTIn this paper we calculate the norm of the bounded composition operator on the Fock space over . This verifies a conjecture posed in Carswell B, MacCluer B, Schuster A. [Composition operators on the Fock space. Acta Sci Math (Szeged). 2003;69:871–887].

On norms of composition operators on weighted hardy spaces

The computation of composition operator on Hardy spaces is very hard. In this paper we propose a norm of a bounded composition operator on weighted Hardy spaces H2(b) induced by a disc automorphism by embedding the classical Hardy space . The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence b. As an application of our results, an estimate for the norm of any bounded composition operator on H2(b) is obtained.

Erratum and addendum to the paper "Compactness and essential norms of composition operators on Orlicz-Lorentz spaces" [Applied Mathematics Letters 25 (2012) 1778--1783

Erratum and addendum to the paper "Compactness and essential norms of composition operators on Orlicz-Lorentz spaces" [Applied Mathematics Letters 25 (2012) 1778--1783

Composition Operators on Cesàro Function Spaces

The compact, invertible, Fredholm, and closed range composition operators are characterized. We also make an effort to compute the essential norm of composition operators on the Cesàro function spaces.

Norms of composition operators on weighted Hardy spaces

The norm of a bounded composition operator induced by a disc automorphism is estimated on weighted Hardy spaces H 2(β) in which the classical Hardy space is continuously embedded. The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence β. As a by-product of our results, an estimate for the norm of any bounded composition operator on H 2(β) is obtained.

A note on the essential norm of composition operators from H p (B N ) to H q (B N )

The authors give an upper bound of the essential norms of composition operators between Hardy spaces of the unit ball in terms of the counting function in the higher dimensional value distribution theory defined by Professor S. S. Chern. The sufficient condition for such operators to be bounded or compact is also given.

Essential norms of composition operators between Bloch type spaces in the polydisk

In 2010, Ruhan Zhao obtained the essential norms of composition operators between Bloch type spaces in the disk by the nth power of the induced analytic function. This paper will generalize Zhao’s results to the polydisk. Unlike the case of the composition operators on the unit disk, the essential norms are different for the cases \({p \in (0,1)}\) and p ≥ 1.

Essential norms of composition operators between weighted bergman spaces of the unit disc

In this paper, we express the essential norms of composition operators between weighted Bergman spaces of the unit disc in terms of the generalized Nevanlinna counting function.

An upper bound of essential norm of composition operator on H 2(B n )

The authors give an upper bound of the essential norm of a composition operator on H2(Bn), which involves the counting function in the higher dimensional value distribution theory defined by S. S. Chern. A criterion is also given to assure that the composition operator on H2(Bn) is bounded or compact.

Essential norm of composition operators on the Hardy space H 1 and the weighted Bergman spaces $${A_{\alpha}^{p}}$$ on the ball

We estimate the essential norm of a composition operator acting on the Hardy space H1 and the weighted Bergman spaces \({A_{\alpha}^{p}}\) on the unit ball. In passing, we recover (and somehow simplify the proof of) parts of the recent article by Demazeux, dealing with the same question for H1 of the unit disc. We also estimate the essential norm of a composition operator acting on \({A_{\alpha}^{p}}\) in terms of the angular derivatives of \({\phi}\), under a mild condition on \({\phi}\).

Essential norms of composition operators between Hardy spaces of the unit disc

The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.

Essential Norm of Composition Operators on Banach Spaces of Hölder Functions

Let(X,d)be a pointed compact metric space, let0&lt;α&lt;1, and letφ:X→Xbe a base point preserving Lipschitz map. We prove that the essential norm of the composition operatorCφinduced by the symbolφon the spaceslip0(X,dα)andLip0(X,dα)is given by the formula‖Cφ‖e=limt→0 sup⁡0&lt;d(x, y)&lt;t(d(φ(x),φ(y))α/d(x,y)α)whenever the dual spacelip0(X,dα)∗has the approximation property. This happens in particular whenXis an infinite compact subset of a finite-dimensional normed linear space.

Norm of composition operators on the Bloch space

The author estimates the semi-norm and norm of composition operators on the Block space; and obtains several necessary conditions for a composition operator to be isometric.

On norms of composition operators acting on Bergman spaces

For arbitrary composition operators acting on a general Bergman space we improve the known lower bound for the norm and also generalize a related recent theorem of D.G. Pokorny and J.E. Shapiro. Next, we obtain a geometric formula for the norms of composition operators with linear fractional symbols, thus extending a result of C. Cowen and P. Hurst and revealing the meaning of their computation. Finally, we obtain a lower bound for essential norm of an arbitrary composition operator related to the well-known criterion of B. MacCluer and J.H. Shapiro. As a corollary, norms and essential norms are obtained for certain univalently induced noncompact composition operators in terms of the minimum of the angular derivative of the symbol.

Norms of Composition Operators on the Hardy Space

We show that the norm of a composition operator on the classical Hardy space H 2 cannot be computed using only the set of H 2 reproducing kernels, answering a question raised by Cowen and MacCluer.