The notion of conjugation is extended to Banach $$*$$ -algebras. The aim of this paper is to characterize conjugations on the Banach algebra of all bounded linear operators on a complex Hilbert space, the algebra of J-symmetric operators on a complex Hilbert space with given conjugation J and the algebra of all complex valued continuous functions, defined on a connected locally compact Hausdorff space, which vanish at infinity.

中文翻译：

---

Banach 上的共轭 $$*$$-代数

共轭的概念被扩展到 Banach $$*$$ -代数。本文的目的是刻画复 Hilbert 空间上所有有界线性算子在 Banach 代数上的共轭、具有给定共轭 J 的复 Hilbert 空间上 J 对称算子的代数以及所有复值连续函数的代数，定义在一个连接的局部紧致 Hausdorff 空间上，该空间在无穷远处消失。