Given a closed densely defined symmetric operator S in a separable Hilbert space, by means of a non-real and non-imaginary complex number z and the corresponding deficiency subspace \({{\mathfrak {N}}}_z\) of S we define a new closed symmetric operator S(z) with dense domain. We prove that the operator S(z) preserves various properties of S. When the deficiency indices of S are equal a bijection of the set of all selfadjoint extensions of S onto the set of all selfadjoint extensions of S(z) is established. We consider in detail the case when a symmetric operator S is nonnegative.

中文翻译：

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对称运算符的克隆

给定一个封闭稠定对称操作者š以可分离Hilbert空间，通过一个非实时和非虚复数的装置Ž和相应的缺乏子空间\（{{\ mathfrak {N}}} _Ž\）的小号我们定义一个新的具有密集域的封闭对称算子S（z）。我们证明了算子S（z）保留S的各种性质。当的不足指数小号是等于设定的所有自伴扩展中的一个双射小号到集合的所有自伴扩展的小号（ž） 成立。我们详细考虑对称算子S为非负数的情况。