Antinormal Weighted Composition Operators

Abstract

Let l 2 = L 2 N, μ, where N is set of all positive integers and μ is the counting measure whose σ -algebra is the power set of N. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space l 2. We also determine a class of antinormal weighted composition operators on Hardy space H 2 D. © 2016 Dilip Kumar and Harish Chandra.