Wandering subspaces and the Beurling type theorem. II

作者：Izuchi Kei Ji^*; Izuchi Kou Hei; Izuchi Yuko

来源：The New York Journal of Mathematics, 2010, 16: 489-505.

• Beurling type theorem
• Hardy space over the bidisk
• invariant subspace
• wandering subspace
• fringe operator

Let H-2 be the Hardy space over the bidisk. Let phi(w) be a nonconstant inner function. We denote by [z - phi(w)] the smallest invariant subspace for both operators T-z and T-w containing the function z - phi(w). Aleman, Richter and Sundberg showed that the Beurling type theorem holds for the Bergman shift on the Bergman space. It is known that the compression operator S-z on H-2 circle minus [z - w] is unitarily equivalent to the Bergman shift, so the Beurling type theorem holds for S-z on H-2 circle minus [z - w]. As a generalization, we shall show that the Beurling type theorem holds for S-z on H-2 circle minus [z - phi(w)]. Also we shall prove that the Beurling type theorem holds for the fringe operator F-w on [z - w] circle minus z[z - w] and for F-z on [z - phi(w)] circle minus w[z - phi(w)] if phi(0) = 0.

• 出版日期2010