On the structure of invariant subspaces for the shift operator on Bergman spaces

2018/06/09 by Liu, Junfeng
#30H10 #32A36 #47A15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1806.03485

Abstract

It is well known that the structure of nontrival invariant subspaces for the shift operator on the Bergman space is extremely complicated and very little is known about their specific structures, and that a complete description of the structure seems unlikely. In this paper, we find that any invariant subspace M(≠ \0\) for the shift operator M_z on the Bergman space A^p_α(\D)~(1≤ p< ∞,~~-1

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