In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundb...In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.展开更多
<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, i...<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, in addition, that for φ,ψ and f in H~∞(D), is unitarily equivalent to M_f iff φ=ψ=f=const. provided some finite condition is satisfied.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 10871083)National Science Foundation of USA (Grant No. 0457285)
文摘In this paper,by lifting the Bergman shift as the compression of an isometry on a subspace of the Hardy space of the bidisk,we give a proof of the Beurling type theorem on the Bergman space of Aleman,Richter and Sundberg(1996) via the Hardy space of the bidisk.
基金Project supported by the National Natural Science Foundation of China.
文摘<正> The notion of super-isometric dilation is introduced and some elementary properties of this dilation are established. It is shown that the Bergman shift is super-isometrically dilatable, and it is proved, in addition, that for φ,ψ and f in H~∞(D), is unitarily equivalent to M_f iff φ=ψ=f=const. provided some finite condition is satisfied.
