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arXiv · 1810.05381

The minimal and maximal symmetries for $J$-contractive projections

Yuan Li·Xiaomei Cai·Jiajia Niu·Jiaxin Zhang
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Abstract

In this paper, we firstly character the structures of symmetries $J$ such that a projection $P$ is $J$-contractive. Then the minimal and maximal elements of the symmetries $J$ with $P^{\ast}JP\leqslant J$(or $JP\geqslant0)$ are given. Moreover, some formulas between $P_{(2I-P-P^{\ast})^{+}}$ $(P_{(2I-P-P^{\ast})^{-}})$ and $P_{(P+P^{\ast})^-}$ $(P_{(P+P^{\ast})^+})$ are established.

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Yuan Li, Xiaomei Cai, Jiajia Niu, Jiaxin Zhang. 2018-10-12. The minimal and maximal symmetries for $J$-contractive projections. https://arxiv.org/abs/1810.05381

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