In this paper we study skew m-complex symmetric operators. In particular, we show that if T ∈ L(H) is a skew m-complex symmetric operator with a conjugation C, then eitT, e−itT, and e−itT ∗ are (m, C)-isometric for every t ∈ R. Moreover, we examine some conditions for skew m-complex symmetric operators to be skew (m − 1)-complex symmetric.
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2010 Mathematics Subject Classification. Primary 47A11, Secondary 47B25. Keywords. Skew m-complex symmetric operator; (m, C)-Isometric operator. Received: 15 October 2018; Accepted: 26 June 2019 Communicated by Dragan S. Djordjević This work was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2016R1D1A1B03931937). 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(2019R1A2C1002653) and this research is partially supported by Grant-in-Aid Scientific Research No.15K04910. Email addresses: email@example.com (Muneo Cho¯), firstname.lastname@example.org (Eungil Ko), email@example.com; firstname.lastname@example.org (Ji Eun Lee)
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- C)-Isometric operator
- Skew m-complex symmetric operator