Fredholm composition operators on Banach spaces of holomorphic functions

2024-03-28 11:26

Speaker: Cao Xuefu

unit: School of Mathematics and Information Science, Guangzhou University

Time: March 29, 2024, from 3:30 pm to 4:30 pm

Venue: Room 314, Building 58, School of Mathematics, Beiyangyuan Campus, Tianjin University

starttime: March 29, 2024, from 3:30 pm to 4:30 pm


Let B(Ω) be a Banach space of holomorphic functions on a bounded connected domain Ω in Cn, which contains the ring of polynomials on Ω. When n > 1, we may assume that Ω is simply connected since any holomorphic function on Ω can be analytically extended to the holes in Ω by Hartogs theorem. Given a holomorphic selfmap φ : Ω → Ω, the composition operator Cφ : B(Ω) → B(Ω) is defined by Cφf=f◦φ,∀f∈B(Ω). We characterize the composition operator Cφ to be a Fredholm operator on B(Ω).

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