scholarly journals A Note on Unbounded Hyponormal Composition Operators inL2-Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Piotr Budzyński
Keyword(s):  
Composition Operator ◽  
Composition Operators

We construct an unbounded hyponormal composition operatorCϕinL2-space such that the domains ofCϕ2andCϕ2are trivial.

scholarly journals Some results on isometric composition operators on Lipschitz spaces

2021 ◽  
Author(s):  
Abraham Rueda Zoca
Keyword(s):  
Convex Hull ◽  
Composition Operator ◽  
Metric Spaces ◽  
Composition Operators ◽  
Extreme Points ◽  
Necessary Condition ◽  
Closed Convex Hull ◽  
Lipschitz Spaces ◽  
Complete Characterisation

AbstractGiven two metric spaces M and N we study, motivated by a question of N. Weaver, conditions under which a composition operator $$C_\phi :{\mathrm {Lip}}_0(M)\longrightarrow {\mathrm {Lip}}_0(N)$$ C ϕ : Lip 0 ( M ) ⟶ Lip 0 ( N ) is an isometry depending on the properties of $$\phi $$ ϕ . We obtain a complete characterisation of those operators $$C_\phi $$ C ϕ in terms of a property of the function $$\phi $$ ϕ in the case that $$B_{{\mathcal {F}}(M)}$$ B F ( M ) is the closed convex hull of its preserved extreme points. Also, we obtain necessary condition for $$C_\phi $$ C ϕ being an isometry in the case that M is geodesic.

scholarly journals COMPOSITION OPERATORS BELONGING TO SCHATTEN CLASS 𝒮p

2010 ◽  
Vol 81 (3) ◽  
pp. 465-472
Author(s):  
CHENG YUAN ◽  
ZE-HUA ZHOU
Keyword(s):  
Bergman Space ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Schatten Class

AbstractWe investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class 𝒮p are obtained. We also construct a compact composition operator which does not belong to any Schatten class.

scholarly journals Composition operators in Orlicz spaces

2004 ◽  
Vol 76 (2) ◽  
pp. 189-206 ◽  
Author(s):  
Yunan Cui ◽  
Henryk Hudzik ◽  
Romesh Kumar ◽  
Lech Maligranda
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Orlicz Spaces

AbstractComposition operators Cτ between Orlicz spaces Lϕ (Ω, Σ, μ) generated by measurable and nonsingular transformations τ from Ω into itself are considered. We characterize boundedness and compactness of the composition operator between Orlicz spaces in terms of properties of the mapping τ, the function ϕ and the measure space (Ω, Σ, μ). These results generalize earlier results known for Lp-spaces.

scholarly journals M-Cohyponormal powers of composition operators

1992 ◽  
Vol 53 (1) ◽  
pp. 9-16
Author(s):  
Satish K. Khurana ◽  
Babu Ram
Keyword(s):  
Composition Operator ◽  
Measure Space ◽  
Composition Operators ◽  
Finite Measure ◽  
Finite Measure Space ◽  
Positive Integers ◽  
Nikodym Derivative

AbstractLet T1, i = 1, 2 be measurable transformations which define bounded composition operators C Ti on L2 of a σ-finite measure space. Let us denote the Radon-Nikodym derivative of with respect to m by hi, i = 1, 2. The main result of this paper is that if and are both M-hyponormal with h1 ≤ M2(h2 o T2) a.e. and h2 ≤ M2(h1 o T1) a.e., then for all positive integers m, n and p, []* is -hyponormal. As a consequence, we see that if is an M-hyponormal composition operator, then is -hyponormal for all positive integers n.

scholarly journals Geometric properties of composition operators belonging to Schatten classes

2001 ◽  
Vol 26 (4) ◽  
pp. 239-248 ◽  
Author(s):  
Yongsheng Zhu
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Schatten Classes ◽  
Geometric Properties ◽  
Image Domain ◽  
Function Mapping

We investigate the connection between the geometry of the image domain of an analytic function mapping the unit disk into itself and the membership of the composition operator induced by this function in the Schatten classes. The purpose is to provide solutions to Lotto's conjectures and show a new compact composition operator which is not in any of the Schatten classes.

Composition operators on weighted spaces of holomorphic functions on the upper half plane

2018 ◽  
Vol 122 (1) ◽  
pp. 141
Author(s):  
Wolfgang Lusky
Keyword(s):  
Half Plane ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Bounded Operator ◽  
Holomorphic Functions ◽  
Weighted Spaces ◽  
Weight Functions ◽  
Spaces Of Holomorphic Functions ◽  
Upper Half Plane

We consider moderately growing weight functions $v$ on the upper half plane $\mathbb G$ called normal weights which include the examples $(\mathrm{Im} w)^a$, $w \in \mathbb G$, for fixed $a > 0$. In contrast to the comparable, well-studied situation of normal weights on the unit disc here there are always unbounded composition operators $C_{\varphi }$ on the weighted spaces $Hv(\mathbb G)$. We characterize those holomorphic functions $\varphi \colon \mathbb G \rightarrow \mathbb G$ where the composition operator $C_{\varphi } $ is a bounded operator $Hv(\mathbb G) \rightarrow Hv(\mathbb G)$ by a simple property which depends only on $\varphi $ but not on $v$. Moreover we show that there are no compact composition operators $C_{\varphi }$ on $Hv(\mathbb G)$.

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.

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

scholarly journals Composition operators on a functional Hilbert space

1979 ◽  
Vol 20 (3) ◽  
pp. 377-384 ◽  
Author(s):  
R.K. Singh ◽  
S.D. Sharma
Keyword(s):  
Hilbert Space ◽  
Lower Bound ◽  
Linear Transformation ◽  
Composition Operator ◽  
Composition Operators ◽  
Bounded Linear ◽  
Functional Hilbert Space ◽  
Bounded Linear Transformation

Let T be a mapping from a set X into itself and let H(X) be a functional Hilbert space on the set X. Then the composition operator CT on H(X) induced by T is a bounded linear transformation from H(X) into itself defined by CTf = f ∘ T. In this paper composition operators are characterized in the case when H(X) = H2(π+) in terms of the behaviour of the inducing functions in the vicinity of the point at infinity. An estimate for the lower bound of ∥CT∥ is given. Also the invertibility of CT is characterized in terms of the invertibility of T.

Commutants of composition operators induced by a parabolic linear fractional automorphisms of the unit disk

2012 ◽  
Vol 15 (1) ◽  
Author(s):  
Yuriy Linchuk
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Analytic Functions ◽  
Composition Operators ◽  
Linear Fractional Transformation ◽  
Space Of Analytic Functions ◽  
Continuous Operators

AbstractThe commutant of composition operator induced by a parabolic linear fractional transformation of the unit disk onto itself in the class of linear continuous operators acting on the space of analytic functions is described.

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