An extremal composition operator on the Hardy space of the bidisk with small approximation numbers

Abstract

We construct an analytic self-map Φ of the bidisk D 2 whose image touches the distinguished boundary, but whose approximation numbers of the associated composition operator on H 2 (D 2 ) are small in the sense that lim sup n→∞ [a n 2 (C Φ )] 1/n < 1.MSC 2010 primary: 47B33 ; secondary: 32A35 ; 46B28