The mean transform and the mean limit of an operator
The mean transform and the mean limit of an operator
复制标题
算子的均值变换和均值极限
DOI：
10.1090/proc/14277
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发表时间：
2018
影响因子：
1
通讯作者：
M. Mbekhta
中科院分区：
文献类型：
--
作者：
F. Chabbabi;E. Curto;M. Mbekhta
设T∈B(H)是Hilbert空间H上的有界线性算子，T≡V|T|是T的极分解，T的平均变换定义为ŷT：=1 2(V|T|+|T|V).本文研究了平均变换的迭代，定义了算子的平均极限作为迭代的极限(按算子范数)。利用原算子，我们得到了均值变换的数值范围和数值半径的新估计。对于一类特殊的单边L加权移位，我们刻画了谱半径与均值极限之间的精确关系，并得到了一些精确的估计。
Let T ∈ B(H) be a bounded linear operator on a Hilbert space H , and let T ≡ V|T | be the polar decomposition of T. The mean transform of T is defined bŷT := 1 2 (V|T |+ |T |V). In this paper we study the iterates of the mean transform and we efine the mean limit of an operator as the limit (in the operator norm) of tho se iterates. We obtain new estimates for the numerical range and numerical radius of th e mean transform in terms of the original operator. For the special class of unilatera l weighted shifts we describe the precise relationship between the spectral radius and the mea n limit, and obtain some sharp estimates.