scholarly journals Composition operators

1978 ◽  
Vol 18 (3) ◽  
pp. 439-446 ◽  
Author(s):  
R.K. Singh ◽  
B.S. Komal
Keyword(s):  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Unit Disc ◽  
Necessary And Sufficient ◽  
Made In

A study of centered composition operators on l2 is made in this paper. Also the spectrum of surjective composition operators is computed. A necessary and sufficient condition is obtained for the closed unit disc to be the spectrum of a surjective composition operator.

scholarly journals Some results on composition operators onℓ2

1979 ◽  
Vol 2 (1) ◽  
pp. 29-34 ◽  
Author(s):  
R. K. Singh ◽  
D. K. Gupta ◽  
B. S. Komal
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bounded Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterised.

scholarly journals Composition operators fromℬαtoQKtype spaces

2008 ◽  
Vol 6 (1) ◽  
pp. 88-104 ◽  
Author(s):  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Analytic Functions ◽  
Composition Operators ◽  
Nondecreasing Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Necessary And Sufficient

Suppose thatϕis an analytic self-map of the unit diskΔ. Necessary and sufficient condition are given for the composition operatorCϕf=fοϕto be bounded and compact fromα-Bloch spaces toQKtype spaces which are defined by a nonnegative, nondecreasing functionk(r)for0≤r<∞. Moreover, the compactness of composition operatorCϕfromℬ0toQKtype spaces are studied, whereℬ0is the space of analytic functions offwithf′∈H∞and‖f‖ℬ0=|f(0)|+‖f′‖∞.

Boundedness from Below of Composition Operators on α-Bloch Spaces

2008 ◽  
Vol 51 (2) ◽  
pp. 195-204 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bloch Spaces ◽  
Necessary And Sufficient ◽  
Bounded Below

AbstractWe give a necessary and sufficient condition for a composition operator on an α-Bloch space with α ≥ 1 to be bounded below. This extends a known result for the Bloch space due to P. Ghatage, J. Yan, D. Zheng, and H. Chen.

scholarly journals Locally Lipschitz Composition Operators in Space of the Functions of BoundedκΦ-Variation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Odalis Mejía ◽  
Nelson José Merentes Díaz ◽  
Beata Rzepka
Keyword(s):  
Lipschitz Condition ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Local Lipschitz Condition ◽  
Locally Lipschitz ◽  
Necessary And Sufficient

We give a necessary and sufficient condition on a functionh:R→Runder which the nonlinear composition operatorH, associated with the functionh,Hu(t)=h(u(t)), acts in the spaceκΦBV[a,b]and satisfies a local Lipschitz condition.

scholarly journals Boundedness of composition operators on Morrey spaces and weak Morrey spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Naoya Hatano ◽  
Masahiro Ikeda ◽  
Isao Ishikawa ◽  
Yoshihiro Sawano
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Morrey Spaces ◽  
Characteristic Functions ◽  
Sufficient Condition ◽  
Specific Function ◽  
Necessary And Sufficient Condition ◽  
Lebesgue Spaces ◽  
Necessary And Sufficient ◽  
Weak Morrey Spaces

AbstractIn this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As this specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.

scholarly journals ON THE COMPLEXITY OF FINDING A NECESSARY AND SUFFICIENT CONDITION FOR BLASCHKE-OSCILLATORY EQUATIONS

2014 ◽  
Vol 57 (3) ◽  
pp. 543-554
Author(s):  
JANNE HEITTOKANGAS ◽  
ATTE REIJONEN
Keyword(s):  
Differential Equation ◽  
Bergman Space ◽  
Nontrivial Solution ◽  
Unit Disc ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Number Of Zeros ◽  
Zero Sequence ◽  
Zeros Of Solutions ◽  
Necessary And Sufficient

AbstractIf A(z) belongs to the Bergman space , then the differential equation f″+A(z)f=0 is Blaschke-oscillatory, meaning that the zero sequence of every nontrivial solution satisfies the Blaschke condition. Conversely, if A(z) is analytic in the unit disc such that the differential equation is Blaschke-oscillatory, then A(z) almost belongs to . It is demonstrated that certain “nice” Blaschke sequences can be zero sequences of solutions in both cases when A ∈ or A ∉ . In addition, no condition regarding only the number of zeros of solutions is sufficient to guarantee that A ∈ .

scholarly journals M-quasi-hyponormal composition operators

1987 ◽  
Vol 10 (3) ◽  
pp. 621-623
Author(s):  
Pushpa R. Suri ◽  
N. Singh
Keyword(s):  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained forM-quasi-hyponormal composition operators. It has also been proved that the class ofM-quasi-hyponormal composition operators coincides with the class ofM-paranormal composition operators. Existence ofM-hyponormal composition operators which are not hyponormal; andM-quasihyponormal composition operators which are notM-hyponormal and quasi-hyponormal are also shown.

scholarly journals An elementary approach to the matricial Nevanlinna–Pick interpolation criterion

1989 ◽  
Vol 32 (1) ◽  
pp. 121-126 ◽  
Author(s):  
S. C. Power
Keyword(s):  
Unit Disc ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Elementary Approach ◽  
Analytic Matrix ◽  
Matrix Contraction ◽  
Image Position ◽  
Necessary And Sufficient ◽  
Pick Matrix

The matricial Nevanlinna–Pick interpolation criterion determines when there is an analytic matrix contraction valued function on the complex unit disc which assumes preassigned n × n matrix values w1,…,wm at preassigned interpolation points z1,…,zm. Taking ∥wi∥ < 1, for i = 1,…,m, the necessary and sufficient condition is the positivity of the nm × nm matricial Pick matrix,

Composition operators between Bergman spaces of logarithmic weights

2015 ◽  
Vol 26 (09) ◽  
pp. 1550068 ◽  
Author(s):  
Ern Gun Kwon ◽  
Jinkee Lee
Keyword(s):  
Integral Representation ◽  
Bergman Space ◽  
Composition Operators ◽  
Counting Function ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Logarithmic Weight

Let [Formula: see text] be the composition operator induced by a holomorphic self-map φ of the open complex unit disk. In this paper, a necessary and sufficient condition for the boundedness of [Formula: see text] from one weighted Bergman space of logarithmic weight into another is described in terms of a growth condition of a generalized counting function for φ. We make use of a new integral representation of a modified counting function which depends on log-convexity of the weight function as well as some estimates for the norm of the weighted Bergman space.

THE ESSENTIAL NORMS OF COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

2018 ◽  
Vol 97 (2) ◽  
pp. 297-307
Author(s):  
YUFEI LI ◽  
YUFENG LU ◽  
TAO YU
Keyword(s):  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Essential Norm ◽  
Angular Derivative ◽  
Dirichlet Spaces ◽  
Closed Unit Disc ◽  
Weighted Dirichlet Spaces

Let $\unicode[STIX]{x1D711}$ be an analytic self-map of the unit disc. If $\unicode[STIX]{x1D711}$ is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator $C_{\unicode[STIX]{x1D711}}$ on the weighted Dirichlet spaces ${\mathcal{D}}_{\unicode[STIX]{x1D6FC}}$ for $\unicode[STIX]{x1D6FC}>0$. We also show that, for a univalent analytic self-map $\unicode[STIX]{x1D711}$ of $\mathbb{D}$, if $\unicode[STIX]{x1D711}$ has an angular derivative at some point of $\unicode[STIX]{x2202}\mathbb{D}$, then the essential norm of $C_{\unicode[STIX]{x1D711}}$ on the Dirichlet space is equal to one.

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