A representation theorem for cyclic analytic two-isometries
A representation theorem for cyclic analytic two-isometries
复制标题
DOI：
10.1090/s0002-9947-1991-1013337-1
复制
发表时间：
1991
影响因子：
1.3
通讯作者：
S. Richter
中科院分区：
文献类型：
--
作者：
S. Richter
复可分Hilbert空间Z上的有界线性算子T称为2-等距算子，如果T* 2 T 2 - 2 T * T+I = O .我们说T是解析的，如果nn，0 Tnt =（0）。本文证明了在Dirichlet型空间D（8）上，每一个循环解析2-等距都可以表示为与z的乘积。这里，ze表示单位圆上的有限正Borel测度。对于两个测度，u和v是在D（8）和D（v）上乘以z得到的2-等距是酉等价的当且仅当u = v。我们还研究了这些2-等距的相似性和拟相似性，并将我们的结果应用于Dirichlet移位的不变子空间。
A bounded linear operator T on a complex separable Hilbert space Z is called a 2-isometry if T*2T2-2T* T+I = O . We say that T is analytic if nn,0 Tnt = (0) . In this paper we show that every cyclic analytic 2-isometry can be represented as multiplication by z on a Dirichlet-type space D(8). Here ,ze denotes a finite positive Borel measure on the unit circle. For two measures ,u and v the 2-isometries obtained as multiplication by z on D(8) and D(v) are unitarily equivalent if and only if ,u = v . We also investigate similarity and quasisimilarity of these 2-isometries, and we apply our results to the invariant subspaces of the Dirichlet shift.