PATH CONNECTED COMPONENTS IN THE SPACES OF NONZERO WEIGHTED COMPOSITION OPERATORS WITH THE STRONG OPERATOR TOPOLOGY I

2016 ◽  
Vol 7 (3) ◽  
pp. 161-176
Author(s):  
Kei Ji Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Composition Operators ◽  
Strong Operator Topology ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
Strong Operator ◽  
Weighted Composition ◽  
Path Connected

Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II

2018 ◽  
Vol 85 (1-2) ◽  
pp. 92
Author(s):  
Kei Ji Izuchi ◽  
Yuko Izuchi
Keyword(s):  
Harmonic Functions ◽  
Composition Operators ◽  
Strong Operator Topology ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
Strong Operator ◽  
Weighted Composition ◽  
Path Connected ◽  
Bounded Harmonic Functions

The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.

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

2019 ◽  
Vol 30 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Le Hai Khoi ◽  
Le Thi Hong Thom ◽  
Pham Trong Tien
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
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.

Iterated Aluthge transforms of composition operators on H2

2015 ◽  
Vol 26 (10) ◽  
pp. 1550079
Author(s):  
Sungeun Jung ◽  
Yoenha Kim ◽  
Eungil Ko
Keyword(s):  
Composition Operators ◽  
Strong Operator Topology ◽  
Weighted Composition Operators ◽  
Strong Operator ◽  
Normal Operators ◽  
Weighted Composition

In this paper, we study various properties of the iterated Aluthge transforms of the composition operators Cφ and Cσ where φ(z) = az + (1 - a) and [Formula: see text] for 0 < a < 1. We express the iterated Aluthge transforms [Formula: see text] and [Formula: see text] as weighted composition operators with linear fractional symbols. As a corollary, we prove that [Formula: see text] and [Formula: see text] are not quasinormal but binormal. In addition, we show that [Formula: see text] and [Formula: see text] are quasisimilar for all non-negative integers n and m. Finally, we show that [Formula: see text] and [Formula: see text] converge to normal operators in the strong operator topology.

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