We investigate the general condition for an operator to be unitary. This condition is introduced according to the definition of the position operator in curved space. In a particular case, we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator. Also we introduce a universal formula for adjoint of an arbitrary linear operator. Our procedure in this paper is totally different from others, as we explore a general approach based only on the algebra of the operators. Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.

中文翻译：

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介绍弯曲空间中算符为酉的一般条件

我们研究了算子是幺正的一般条件。这个条件是根据弯曲空间位置算子的定义引入的。在特定情况下，我们讨论了弯曲空间中平移算子的概念，然后讨论了它与反厄米生成器的关系。我们还为任意线性算子的伴随引入了一个通用公式。我们在本文中的程序与其他程序完全不同，因为我们探索了一种仅基于算子代数的通用方法。我们的方法仅针对一维空间中的翻译算子进行讨论，而不针对一般算子进行讨论。