Isometries of the product of composition operators on weighted Bergman space

Counter Example ◽

Multiplicative Operator ◽

In this paper, the necessary and sufficient conditions for the product of composition operators to be isometry are obtained on weighted Bergman space. With the help of a counter example we also proved that unlike on [Formula: see text] and [Formula: see text] the composition operator on [Formula: see text] induced by an analytic self-map on [Formula: see text] with fixed origin need not be of norm one. We have generalized the Schwartz’s [Composition operators on [Formula: see text], thesis, University of Toledo (1969)] well-known result on [Formula: see text] which characterizes the almost multiplicative operator on [Formula: see text]

Normal and quasinormal weighted composition operators

Glasgow Mathematical Journal ◽

10.1017/s0017089500008338 ◽

1991 ◽

Vol 33 (3) ◽

pp. 275-279 ◽

Cited By ~ 4

Author(s):

James T. Campbell ◽

Mary Embry-Wardrop ◽

Richard J. Fleming ◽

S. K. Narayan

Keyword(s):

Composition Operator ◽

Composition Operators ◽

Weighted Composition Operator ◽

Sufficient Conditions ◽

The Other ◽

Weighted Composition ◽

In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class.

COMPACT DIFFERENCES OF COMPOSITION OPERATORS ON BERGMAN SPACES IN THE BALL

Journal of the Australian Mathematical Society ◽

10.1017/s1446788711001091 ◽

2010 ◽

Vol 89 (3) ◽

pp. 407-418 ◽

Cited By ~ 4

Author(s):

XIANG DONG YANG ◽

LE HAI KHOI

Keyword(s):

Unit Ball ◽

Composition Operator ◽

Composition Operators ◽

Bergman Spaces ◽

Sufficient Conditions ◽

Compact Operators ◽

Weighted Bergman Spaces ◽

Finite Sum ◽

AbstractWe obtain necessary and sufficient conditions for the compactness of differences of composition operators acting on the weighted Bergman spaces in the unit ball. A representation of a composition operator as a finite sum of composition operators modulo compact operators is also studied.

Multiplication Operator with BMO Symbols and Berezin Transform

Journal of Function Spaces ◽

10.1155/2015/754646 ◽

2015 ◽

Vol 2015 ◽

pp. 1-4

Author(s):

Xue Feng ◽

Kan Zhang ◽

Jianguo Dong ◽

Xianmin Liu ◽

Chi Guan

Keyword(s):

Unit Ball ◽

Bergman Space ◽

Sufficient Conditions ◽

Multiplication Operator ◽

Berezin Transform ◽

Weighted Bergman Space ◽

Special Symbol ◽

We discuss multiplication operator with a special symbol on the weighted Bergman space of the unit ball. We give the necessary and sufficient conditions for the compactness of multiplication operator on the weighted Bergman space of the unit ball.

Commuting Quasihomogeneous Toeplitz Operator and Hankel Operator on Weighted Bergman Space

Abstract and Applied Analysis ◽

10.1155/2013/408168 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8

Author(s):

Jun Yang

Keyword(s):

Toeplitz Operator ◽

Bergman Space ◽

Hankel Operator ◽

Sufficient Conditions ◽

Weighted Bergman Space ◽

Necessary And Sufficient ◽

Quasihomogeneous Symbols

We characterize the commuting Toeplitz operator and Hankel operator with quasihomogeneous symbols. Also, we use it to show the necessary and sufficient conditions for commuting Toeplitz operator and Hankel operator with ordinary functions.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽

10.2298/fil1709877s ◽

2017 ◽

Vol 31 (9) ◽

pp. 2877-2889 ◽

Cited By ~ 1

Author(s):

Amir Sanatpour ◽

Mostafa Hassanlou

Keyword(s):

Composition Operators ◽

Sufficient Conditions ◽

Essential Norm ◽

Norm Estimates ◽

Type Spaces ◽

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

Hyponormality of Toeplitz operators with non-harmonic symbols on the Bergman spaces

Journal of Inequalities and Applications ◽

10.1186/s13660-021-02602-1 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Sumin Kim ◽

Jongrak Lee

Keyword(s):

Toeplitz Operator ◽

Bergman Space ◽

Toeplitz Operators ◽

Bergman Spaces ◽

Sufficient Conditions ◽

AbstractIn this paper, we present some necessary and sufficient conditions for the hyponormality of Toeplitz operator $T_{\varphi }$ T φ on the Bergman space $A^{2}(\mathbb{D})$ A 2 ( D ) with non-harmonic symbols under certain assumptions.

Weighted composition operators between Fock spaces ℱ∞(ℂ) and ℱp(ℂ)

International Journal of Mathematics ◽

10.1142/s0129167x19500150 ◽

2019 ◽

Vol 30 (03) ◽

pp. 1950015 ◽

Cited By ~ 1

Author(s):

Le Hai Khoi ◽

Le Thi Hong Thom ◽

Pham Trong Tien

Keyword(s):

Composition Operators ◽

Sufficient Conditions ◽

Connected Components ◽

Fock Spaces ◽

Weighted Composition ◽

Necessary And Sufficient ◽

Path Connected

In this paper, we establish necessary and sufficient conditions for boundedness and compactness of weighted composition operators acting between Fock spaces [Formula: see text] and [Formula: see text]. We also give complete descriptions of path connected components for the space of composition operators and the space of nonzero weighted composition operators in this context.

Composition operators on μ-Bloch spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-2009-003-1 ◽

2009 ◽

Vol 61 (1) ◽

pp. 50-75 ◽

Cited By ~ 20

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 ◽

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.

New additive results for Cauchy dual and MP-inverse of weighted composition operators

Filomat ◽

10.2298/fil2107215s ◽

2021 ◽

Vol 35 (7) ◽

pp. 2215-2230

Author(s):

Morteza Sohrabi

Keyword(s):

Composition Operators ◽

Sufficient Conditions ◽

Weighted Composition ◽

In this paper, we prove some basic results for Cauchy dual of weighted composition operators. Also we introduce some new classes of operators, called ?-hyponormal, ?-quasi-hyponormal, and we provide necessary and sufficient conditions for Cauchy dual and MP-inverse of weighted composition operators on L2(?) to belong to these classes. In addition, we study the complex symmetry of these types of operators. Moreover, some examples are provided to illustrate the obtained results.

Weighted composition operators from Bloch-type into Bers-type spaces

Creative Mathematics and Informatics ◽

10.37193/cmi.2020.02.16 ◽

2021 ◽

Vol 29 (2) ◽

pp. 243-250

Author(s):

HAMID VAEZI ◽

MOHAMAD NAGHLISAR

Keyword(s):

Composition Operator ◽

Composition Operators ◽

Weighted Composition Operator ◽

Sufficient Conditions ◽

Type Space ◽

Bloch Type Space ◽

Type Spaces ◽

Weighted Composition ◽

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.