We investigate the orthogonality preserving property for pairs of operators on inner product \(C^*\)-modules. Employing the fact that the \(C^*\)-valued inner product structure of a Hilbert \(C^*\)-module is determined essentially by the module structure and by the orthogonality structure, pairs of linear and local orthogonality-preserving operators are investigated, not a priori bounded. We obtain that if \({\mathscr {A}}\) is a \(C^{*}\)-algebra and \(T, S:{\mathscr {E}}\rightarrow {\mathscr {F}}\) are two bounded \({{\mathscr {A}}}\)-linear operators between full Hilbert \({\mathscr {A}}\)-modules, then \(\langle x, y\rangle = 0\) implies \(\langle T(x), S(y)\rangle = 0\) for all \(x, y\in {\mathscr {E}}\) if and only if there exists an element \(\gamma \) of the center \(Z(M({{\mathscr {A}}}))\) of the multiplier algebra \(M({{\mathscr {A}}})\) of \({{\mathscr {A}}}\) such that \(\langle T(x), S(y)\rangle = \gamma \langle x, y\rangle \) for all \(x, y\in {\mathscr {E}}\). Varying the conditions on the operators T and S we obtain further affirmative results for local operators and for pairs of a bounded and an unbounded \({{\mathscr {A}}}\)-linear operator with bounded inverse.

我们研究内积\（C ^ * \）-模块上算子对的正交性。利用一个事实，希尔伯特\（C ^ * \）-模块的\（C ^ * \）值内积结构基本上由模块结构和正交性结构，线性和局部正交性对确定对运算符进行了调查，而不是先验地界。如果\（{\ mathscr {A}} \）是\（C ^ {*} \）-代数和\（T，S：{\ mathscr {E}} \ rightarrow {\ mathscr {F} } \）是完整Hilbert \（{{mathscr {A}} \）-）模块之间的两个有界\（{{\ mathscr {A}}} \）-线性算子，然后\（\ langle x，y \ rangle = 0 \）表示\ {x，y \ in {\ mathscr {E}}中的所有\（\ langle T（x），S（y）\ rangle = 0 \））当且仅当存在一个元素（\伽马\）\中心的ž\（（M - （{{\ mathscr {A}}}））\）乘法器代数\（M（{{\ mathscr { A}}}）\）的\（{{\ mathscr {A}}} \），使得\（\ langle T（X），S（y）的\ rangle = \伽马\ langle的x，y \ rangle \）对于所有\（x，y \ in {\ mathscr {E}} \）。改变运算符T和S的条件，我们将为本地运算符以及有界和无界\（{{\ mathscr {A}}} \）对获得进一步的肯定结果-有界逆的线性算子。