$k$-hyponormality of finite rank perturbations of unilateral weighted shifts
$k$-hyponormality of finite rank perturbations of unilateral weighted shifts
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DOI：
10.1090/s0002-9947-05-04029-8
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发表时间：
2005-06
影响因子：
1.3
通讯作者：
R. Curto;W. Lee
中科院分区：
文献类型：
--
作者：
R. Curto;W. Lee
In this paper we explore finite rank perturbations of unilateral weighted shifts W α . First, we prove that the subnormality of W α is never stable under nonzero finite rank perturbations unless the perturbation occurs at the zeroth weight. Second, we establish that 2-hyponormality implies positive quadratic hyponormality, in the sense that the Maclaurin coefficients of D n (s):= det P n [(W α + sW 2 α )*, W α + sW 2 α ]P n are nonnegative, for every n > 0, where P n denotes the orthogonal projection onto the basis vectors {e 0 , ..., e n }. Finally, for α strictly increasing and W α 2-hyponormal, we show that for a small finite-rank perturbation a' of a, the shift W α , remains quadratically hyponormal.
