On $${m}$$m-Complex Symmetric Operators II
On $${m}$$m-Complex Symmetric Operators II
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DOI：
10.1007/s00009-016-0683-y
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发表时间：
2016-05
影响因子：
1.1
通讯作者：
M. Chō;Eungil Ko;J. Lee
中科院分区：
文献类型：
--
作者：
M. Chō;Eungil Ko;J. Lee
In this paper, we study the structure ofdefined by the following: $${\Delta_m(T):=\sum_{j=0}^{m}(-1)^{m-j} \begin{pmatrix} m \cr j \end{pmatrix}{T^{\ast}}^{j}C{T}^{m-j}C}$$. In particular, we prove that ifis even, thenis complex symmetric with the conjugation, and ifis odd, thenis skew complex symmetric with the conjugation. Moreover, we investigate the conditions for ()-complex symmetric operators to be-complex symmetric operators and characterize the spectrum of. Finally, we show that ifis Hermitian oris-hyponormal, thenimplies.
In this paper, we study the structure ofdefined by the following: $${\Delta_m(T):=\sum_{j=0}^{m}(-1)^{m-j} \begin{pmatrix} m \cr j \end{pmatrix}{T^{\ast}}^{j}C{T}^{m-j}C}$$. In particular, we prove that ifis even, thenis complex symmetric with the conjugation, and ifis odd, thenis skew complex symmetric with the conjugation. Moreover, we investigate the conditions for ()-complex symmetric operators to be-complex symmetric operators and characterize the spectrum of. Finally, we show that ifis Hermitian oris-hyponormal, thenimplies.