Abstract
In this paper, we study the spectral properties of m-complex symmetric operators. In particular, we prove that if T is m-complex symmetric with conjugation C, then T n is also m-complex symmetric with conjugation C for any \({n\in \mathbb{N}}\) . Moreover, if T is m-complex symmetric with conjugation C, then T is decomposable if and only if \({T^{\ast}}\) has the property (\({\beta}\)). As some applications, we give several examples of m-complex symmetric operators with conjugation C.
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This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government MSIP (2009-0083521). The third author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A3006841) and this research is partially supported by Grant-in-Aid Scientific Research No.15K04910.
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Chō, M., Ko, E. & Lee, J.E. On m-Complex Symmetric Operators. Mediterr. J. Math. 13, 2025–2038 (2016). https://doi.org/10.1007/s00009-015-0597-0
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DOI: https://doi.org/10.1007/s00009-015-0597-0