Iranian Mathematical Society Journal of the Iranian Mathematical Society 2717-1612 4 1 2023 01 01 Two classes of $J$-operators 45 54 172063 10.30504/jims.2023.395366.1111 EN T. Ando Hokkaido University (Emeritus), Sapporo, Japan Journal Article 2023 05 01 We define two classes ${\mathfrak A}$ and ${\mathfrak B}$ in the space ${\mathcal B}({\mathcal H})$ of operators acting on a Hilbert space on the basis of $J$-order relation and spectra, and discuss various properties related to these classes. $J$-self-adjoint matrix $J$-order $J$-bicontraction https://jims.ims.ir/article_172063_6b22389a0ee0988d351875274909b5ae.pdf