A class of weighted composition operators whose Range and Null spaces are complemented

2024/02/14 by Patel, Anurag Kumar
#46B25 #47A53 #47B33 #54B15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2402.08972

Abstract

In this paper, we prove that the null space of a weighted composition operator on ℓ_p~ (1 ≤ p < ∞) is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on ℓ_p whose range space is of finite co-dimension. Thereafter, we characterize a class of weighted composition operators whose range space is a complemented subspace. Lastly, we characterize weighted composition operators on ℓ_p which are Fredholm operators.

Related

• Weighted composition operators on the Fock space
• Finite sum of weighted composition operators with closed range
• Weighted composition operators between different Fock spaces
• Weighted composition operators between Fock spaces in several variables
• Weighted composition operators on weighted Fock spaces