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论文类型：期刊论文

发表时间：2020-01-01

发表刊物：JOURNAL OF FUNCTIONAL ANALYSIS

收录刊物：SCIE

卷号：278

期号：1

ISSN号：0022-1236

关键字：Beurling type quotient module; Compressed shift operator; Reducibility

摘要：In this paper, we study the compressed shift operator S-z1, on the Beurling-type quotient module k(theta) of Hardy space H-2(D-2) over the bidisk. Firstly, we give a necessary and sufficient condition such that S z , has nontrivial pure isometry reducing subspace. As an application, we show that S-z1, has Agler reducing subspaces if and only if theta is the product of two one variable inner functions. Secondly, for a rational inner function with degree (n, 1), we show that S-z1, is reducible on k(theta) if and only if S-z1, has Agler reducing subspaces. Furthermore, we study the case when the rational inner functions have degree (n, 2), and this case is quite different from that the degree of theta is (n, 1). (C) 2019 Elsevier Inc. All rights reserved.