scholarly journals Numerical Ranges of Normal Weighted Composition Operators on the Fock Space of CN

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Lili Lang ◽  
Liankuo Zhao
Keyword(s):  
Fock Space ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

Numerical ranges of normal weighted composition operators on the Fock space of CN are completely characterized. The main result shows that numerical ranges of such operators are closely related to their composition symbols.

scholarly journals Invertible Weighted Composition Operators on the Fock Space ofCN

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Liankuo Zhao
Keyword(s):  
Fock Space ◽  
Composition Operators ◽  
Complete Characterization ◽  
Weighted Composition Operators ◽  
Weighted Composition

We give a complete characterization of bounded invertible weighted composition operators on the Fock space ofCN.

scholarly journals Convex-Cyclic Weighted Composition Operators and Their Adjoints

2021 ◽  
Vol 18 (4) ◽  
Author(s):  
Tesfa Mengestie
Keyword(s):  
Complex Plane ◽  
Pointwise Convergence ◽  
Convex Sets ◽  
Fock Space ◽  
Composition Operators ◽  
Invariant Subspaces ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Convergence Topology

AbstractWe characterize the convex-cyclic weighted composition operators $$W_{(u,\psi )}$$ W ( u , ψ ) and their adjoints on the Fock space in terms of the derivative powers of $$ \psi $$ ψ and the location of the eigenvalues of the operators on the complex plane. Such a description is also equivalent to identifying the operators or their adjoints for which their invariant closed convex sets are all invariant subspaces. We further show that the space supports no supercyclic weighted composition operators with respect to the pointwise convergence topology and, hence, with the weak and strong topologies, and answers a question raised by T. Carrol and C. Gilmore in [5].

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