Properties of m-complex symmetric operators

Properties of m-complex symmetric operators
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DOI：
10.24193/subbmath.2017.2.09
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发表时间：
2017-05
期刊：
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影响因子：
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通讯作者：
M. Chō;Eungil Ko;Ji-Eun Lee
M. Chō;Eungil Ko;Ji-Eun Lee
中科院分区：
其他
文献类型：
--
作者：
M. Chō;Eungil Ko;Ji-Eun Lee

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本文研究了$m$-复对称算子的几个性质。特别地，我们证明了：如果{CAL L(H)}$中的$T是$m$-复对称算子，且$N$是$n&gt；2$阶幂零算子且$Tn=Nt$，则$T+N$是$(2n+m-2)$-复对称算子。此外，我们还研究了$T+A$和$TA$的可分解性，其中$T$是$m$-复对称算子，$A$是代数算子。最后，给出了这类算子的各种谱关系。作为这些结果的一些应用，我们讨论了这类算子的Weyl型定理。
In this paper, we study several properties of $m$-complex symmetric operators. In particular, we prove that if $T\in{\cal L(H)}$ is an $m$-complex symmetric operator and $N$ is a nilpotent operator of order $n>2$ with $TN=NT$, then $T+N$ is a $(2n+m-2)$-complex symmetric operator. Moreover, we investigate the decomposability of $T+A$ and $TA$ where $T$ is an $m$-complex symmetric operator and $A$ is an algebraic operator. Finally, we provide various spectral relations of such operators. As some applications of these results, we discuss Weyl type theorems for such operators.