Continuity of the Spectrum of a Field of Self-Adjoint Operators
Continuity of the Spectrum of a Field of Self-Adjoint Operators
复制标题
自伴算子域谱的连续性
DOI：
10.1007/s00023-016-0496-3
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J. Bellissard
中科院分区：
文献类型：
--
作者：
Siegfried Beckus;J. Bellissard
给出了拓扑空间T中以参数t为指标的自伴算子族{（A_t）_{t \in T}}$$（At）t∈T，其谱$${\sigma（A_t）}$$σ（At）关于t是Vietoris连续的充要条件.等价地，边界和差距边在t上是连续的。如果（T，d）是一个度量为d的完备度量空间，这些条件被推广以保证谱边界和谱间隙边的Hölder连续性。作为一个推论，上界提供的大小关闭差距。
Given a family of self-adjoint operators $${(A_t)_{t \in T}}$$(At)t∈T indexed by a parameter t in some topological space T, necessary and sufficient conditions are given for the spectrum $${\sigma(A_t)}$$σ(At) to be Vietoris continuous with respect to t. Equivalently the boundaries and the gap edges are continuous in t. If (T, d) is a complete metric space with metric d, these conditions are extended to guarantee Hölder continuity of the spectral boundaries and of the spectral gap edges. As a corollary, an upper bound is provided for the size of closing gaps.