WEIGHTED SHIFT OPERATORS AND ANALYTIC FUNCTION THEORY
WEIGHTED SHIFT OPERATORS AND ANALYTIC FUNCTION THEORY
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DOI：
10.1090/surv/013/02
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发表时间：
1974
期刊：
影响因子：
--
通讯作者：
A. Shields
中科院分区：
文献类型：
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作者：
A. Shields
1. Introduction. A weighted shift operator T on (complex) Hilbert space H is an operator that maps each vector in some orthonormal basis {en} into a scalar multiple of the next vector (1) Ten= we Wnen+ 1 for all n. If the index n runs over the nonnegative integers, then T is called a unilateral weighted shift, while if n runs over all integers, then T is called a bilateral weighted shift. We shall treat both cases. In the main part of the article we shall not try to assign credits for most of the results. At the end we shall say something about the history of the subject. The reader is assumed to be familiar with the elementary facts about operators on Hilbert space. Also, some basic facts from the theory of commutative Banach algebras with identity are used, as are some facts about analytic functions of one complex variable.
