In this paper we study characterizations of a complex symmetric truncated shift type operator matrix and the Aluthge transform, the Duggal transform, the mean transform, and the generalized mean transform of such an operator matrix T (see (2.1) or (2.2)). As some applications of our main results, we give several examples of truncated shift type operator matrices.
Bibliographical noteFunding Information:
These authors contributed equally to this work. The first named author was partially supported by Labex CEMPI (ANR-11-LABX-0007-01). The second author is partially supported by Grant-in-Aid Scientific Research No. 15K04910. The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058633). The fourth author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2022R1H1A2091052).
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
- Aluthge transform
- Duggal transform
- complex symmetric operator matrix