In this paper, some sufficient and necessary conditions for TB=AB0D\documentclass[12pt]{minimal}
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\begin{document}$$T_{B}=\begin{bmatrix}A &{} B\\ 0 &{} D \\ \end{bmatrix}$$\end{document} in H⊕K\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal H \oplus \mathcal K$$\end{document} to be Kato nonsingular for some closable operator B with D(B)⊃D(D)\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal D(B)\supset \mathcal D(D)$$\end{document} are characterized, where A and D are given closed operators, and H\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal H$$\end{document} and K\documentclass[12pt]{minimal}
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\begin{document}$$\mathcal K$$\end{document} are Hilbert spaces. The properties of regular spectrum σg(TB)\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _{g}(T_{B})$$\end{document} of closed operator matrix TB\documentclass[12pt]{minimal}
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\begin{document}$$T_{B}$$\end{document} are also studied and some sufficient and necessary conditions for σg(TB)=σg(A)∪σg(D)\documentclass[12pt]{minimal}
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\begin{document}$$\sigma _{g}(T_{B})=\sigma _{g}(A)\cup \sigma _{g}(D)$$\end{document} are given. In addition, the corresponding properties of regular spectrum of upper triangular Hamiltonian operator matrix are obtained.
