arXiv subjects

Jiajia Niu

Publications and source records attributed to Jiajia Niu.

2 recordsLinked to original sources

arXiv2019

The minus order for idempotents

Let $P$ and $Q$ be idempotents on a Hilbert space $\mathcal{H}.$ The minus order $P\preceq Q$ is defined by the equation $PQ=QP=P.$ In this note, we first present some necessary and sufficient conditions for which the supremum and infimum of idempotents $P$ and $Q$ exist with respect to the minus order. Also, some properties of the minimum $Q^{or}$ are characterized, where $Q^{or}$=min $\{P^{'}: P^{'}$ is an orthogonal projection on $\mathcal{H}$ with $Q \preceq P^{'} \}.$

math.FA↗

arXiv2018

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

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.

math.FA↗