# 预告：徐小明博士谈“Symmetries for $J$-projection”

时 间：11月11日（周一）10：00-10：30

地 点：仓前校区勤园21-306

主讲人：徐小明，上海应用技术大学澳门金沙国际副院长。主持国家基金1项，已在知名数学杂志上发表SCI论文多篇。

内容概况：Let $\mathcal{B(H)}$ be the algebra of all bounded linear operators on a separable complex Hilbert space $\mathcal{H}.$ We introduce the $J$-decomposition property for projections in $\mathcal{B(H)},$ and prove that the projection $E$ in $\mathcal{B(H)}$ has $J$-decomposition property with respect to a particular space decomposition, which is related to Halmos' two projections theory. Using this, we characterize symmetries $J$ such that the given projection $E$ is a $J$-projection (or $J$-positive projection, or $J$-negative projection). In consequence we study the related properties of symmetries for $J$-projection.

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