Self-adjoint operators in smooth Banach spaces have been already defined in recent works. Here, we extend the concept of adjoint of an operator to the scope of (non-necessarily Hilbert) Banach spaces, obtaining in particular the notion of self-adjoint operator in the non-smooth case. As a consequence, we define the probability density operator on Banach spaces and verify most of its well-known properties.

中文翻译：

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Banach 空间上算子的伴随

光滑巴纳赫空间中的自伴算子已在最近的工作中定义。在这里，我们将算子伴随的概念扩展到（不一定是希尔伯特）Banach 空间的范围，特别是在非光滑情况下获得自伴随算子的概念。因此，我们在 Banach 空间上定义了概率密度算子，并验证了它的大部分众所周知的性质。