Yuan Li, Xiaomei Cai, Shuaijie Wang
Published 2018-06-14Version 1
In this paper, we consider the formulas of the absolute value $|Q_{\lambda,\mu}|,$ where $Q_{\lambda,\mu} = \left(\begin{array}{cc}\lambda I&P P^*&\mu I\end{array}\right): \mathcal{H} \oplus \mathcal{K}$ is self-adjoint operators in the Hilbert space $\mathcal{H}\oplus\mathcal{K}.$ Then the positive parts and the cover projections of $Q_{\lambda,0}$ are obtained. Also, we character the symmetry $J$ such that a projection $P$ is the $J$-projection. In particular, the minimal element of the symmetry $J$ with $JP\geqslant0$ is given.
On the essential spectrum of the sum of self-adjoint operators and the closedness of the sum of operator ranges
Numerical radius inequalities of operator matrices using $(α,β)$-norm
On the reduction of powers of self-adjoint operators
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