When does the Weyl-von Neumann Theorem hold?
When does the Weyl-von Neumann Theorem hold?
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韦尔-冯·诺依曼定理什么时候成立？
DOI：
10.1112/blms.12064
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发表时间：
2017
影响因子：
0.9
通讯作者：
Matsuzawa Yasumichi
中科院分区：
文献类型：
--
作者：
Ando Hiroshi;Matsuzawa Yasumichi
魏尔和冯·诺依曼的一个著名定理断言，两个有界自伴算子模紧酉等价，当且仅当它们的本质谱一致。上述定理对无界算子不成立。然而，存在闭子集，Weyl-von Neumann定理成立：所有（不一定有界）具有本质谱的自伴算子模紧是酉等价的。在本文中，我们确定了满足这一性质。
A famous theorem due to Weyl and von Neumann asserts that two bounded self‐adjoint operators are unitarily equivalent modulo the compacts, if and only if their essential spectrum agree. The above theorem does not hold for unbounded operators. Nevertheless, there exist closed subsetsofon which the Weyl–von Neumann Theorem hold: all (not necessarily bounded) self‐adjoint operators with essential spectrumare unitarily equivalent modulo the compacts. In this paper, we determine exactly whichsatisfies this property.