Approximation numbers of differences of composition operators

Abstract: In this study we consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H 2 (D). We obtain both upper and lower bounds for these approximation numbers and by applying these general results to composition operators with specific types of symbols, we demonstrate the effect of boundary behaviour over the approximation numbers. Moreover, we use these one-dimensional methods and examples to understand the approximation numbers of differences of composition operators acting on the space H 2 (D 2 ) of the bidisc.