Convergence of Iterates of Normal Operators in L^2 Spaces

Abstract

Let (Ω, Σ, m) be a measure space with m being an σ-finite positive measure and let N be a normal operator on L2(Ω, Σ, m). In this note, we study strong and almost everywhere convergences of the sequences {ϕ (N)nf}n∈N in L2(Ω, Σ, m) spaces, where ϕ is a continuous function on the spectrum of N.

Keywords

• L 2 -space
• normal operator
• norm convergence
• almost everywhere convergence.

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