PATH CONNECTED COMPONENTS IN THE SPACE OF WEIGHTED COMPOSITION OPERATORS ON THE DISK ALGEBRA

2012 ◽  
Vol 112A (2) ◽  
pp. 59-77
Author(s):  
Kei Ji Izuchi ◽  
Yuko Izuchi ◽  
Shûichi Ohno
Keyword(s):  
Composition Operators ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
Disk Algebra ◽  
Weighted Composition ◽  
Path Connected

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.

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.

scholarly journals SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

2012 ◽  
Vol 55 (1) ◽  
pp. 229-239 ◽  
Author(s):  
KEI JI IZUCHI ◽  
KOU HEI IZUCHI ◽  
YUKO IZUCHI
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Disk Algebra ◽  
Weighted Composition ◽  
Little Bloch Space

AbstractLet COP =0∩H∞, where0is the little Bloch space on the open unit disk, andA() be the disk algebra on. For non-zero functionsu1,u2,. . .,uN∈A() and distinct analytic self-maps ϕ1,ϕ2,. . .,ϕNsatisfying ϕj∈A() and ∥ϕj∥∞=1 for everyj, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕjmaps COP intoA().

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