论文标题
c* - 代理中的半芬德霍尔姆理论
Semi-Fredholm theory in C*-algebras
论文作者
论文摘要
凯基奇（Keckic）和拉索维奇（Lazovic）通过考虑在Unital c*-Algebra中考虑Fredholm型元素作为C*-Fredholm操作员在标准的Hilbert C* - Mishchenko and Fomenko和Fomenko和Foredbrean profents infinbre infinder infins of and On ne ne ne ne ne ne ne ne ne offin and On ne of and On ne ne-by的概述中，提出了一种公理的方法。布鲁尔。在本文中，我们在Unital c*代数中建立了半杂种理论，作为Keckic和Lazovic方法的延续。我们介绍了半芬霍尔姆型元素和半透明型元素的概念。我们证明，在规范拓扑结构中，一组半 - 弗雷德元素与一组半脉冲元素之间的差异是开放的，即在有限型元素扰动下，一组半透明元素是不变的，以及其他几个结果概括了他们的经典元素。此外，我们说明了结果在适当无限的von Neumann代数的特殊情况下的应用，并在此环境中获得了刺破邻域定理的概括。
Keckic and Lazovic introduced an axiomatic approach to Fredholm theory by considering Fredholm-type elements in an unital C*-algebra as a generalization of C*-Fredholm operators on the standard Hilbert C*-module introduced by Mishchenko and Fomenko and of Fredholm operators on a properly infinite von Neumann algebra introduced by Breuer. In this paper, we establish the semi-Fredholm theory in unital C*-algebras as a continuation of the approach by Keckic and Lazovic. We introduce the notion of semi-Fredholm-type elements and semi-Weyl-type elements. We prove that the difference between the set of semi-Fredholm elements and the set of semi-Weyl elements is open in the norm topology, that the set of semi-Weyl elements is invariant under perturbations by finite type elements, and several other results generalizing their classical counterparts. Also, we illustrate applications of our results to the special case of properly infinite von Neumann algebras and we obtain a generalization of the punctured neighborhood theorem in this setting.
