In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert C*-modules replacing scalars by the center of the algebra, and show that most relations between these spectra are still true for these generalized versions. The relation between these spectra of an operator and those of its compressions is also transferred to the case of Hilbert C*-modules.

中文翻译：

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关于 $$C^{*}$$C∗-代数上算子的压缩和广义谱

在经典算子理论中，有几个版本的谱，与特殊类别的算子（Fredholm、semi-Fredholm、upper/lower semi-Fredholm 等）有关。我们将这些概念推广到希尔伯特 C* 模上的伴随算子，用代数中心代替标量，并表明这些谱之间的大多数关系对于这些广义版本仍然成立。算子的这些谱与其压缩的谱之间的关系也转移到 Hilbert C*-模的情况。