Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces

2012 ◽  
Vol 55 (2) ◽  
pp. 441-448 ◽  
Author(s):  
Nina Zorboska
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Closed Range ◽  
Type Spaces

AbstractWhile there is a large variety of univalently induced closed range composition operators on the Bloch space, we show that the only univalently induced, closed range, composition operators on the Bloch-type spaces Bα with α ≠ 1 are the ones induced by a disc automorphism.

scholarly journals Isometric and Closed-Range Composition Operators between Bloch-Type Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Nina Zorboska
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Function Spaces ◽  
Complete Characterization ◽  
Closed Range ◽  
Different Types ◽  
Type Spaces ◽  
Range Determination

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.

Closed-Range Composition Operators on $${\mathbb{A}^2}$$ and the Bloch Space

2010 ◽  
Vol 68 (4) ◽  
pp. 503-517 ◽  
Author(s):  
John R. Akeroyd ◽  
Pratibha G. Ghatage ◽  
Maria Tjani
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Closed Range

scholarly journals Composition operators with closed range on the Bloch space

2000 ◽  
Vol 129 (7) ◽  
pp. 2039-2044 ◽  
Author(s):  
Pratibha Ghatage ◽  
Jun Yan ◽  
Dechao Zheng
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Closed Range

scholarly journals WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL

2008 ◽  
Vol 19 (08) ◽  
pp. 899-926 ◽  
Author(s):  
ZE-HUA ZHOU ◽  
REN-YU CHEN
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

scholarly journals Weighted Differentiation Composition Operators to Bloch-Type Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Junming Liu ◽  
Zengjian Lou ◽  
Ajay K. Sharma
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Type Spaces

We characterized the boundedness and compactness of weighted differentiation composition operators from BMOA and the Bloch space to Bloch-type spaces. Moreover, we obtain new characterizations of boundedness and compactness of weighted differentiation composition operators.

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