摘要： A KMS matrix is one of the formJ_(n)(a)=[arrayccccc 0 & a & a² &... & aⁿ⁻¹ & 0 & a & ⋱ & ⋮ & & ⋱ & ⋱ & a² & & & ⋱ & a 0 & & & & 0array]forn≥ 1andainℂ . Among other things, we prove the following properties of its numerical range: (1)W(J_(n)(a))is a circular disc if and only ifn=2anda≠ 0 , (2) its boundary∂ W(J_(n)(a))contains a line segment if and only ifn≥ 3and|a|=1 , and (3) the intersection of the boundaries∂ W(J_(n)(a))and∂ W(J_(n)(a)[j])is either the singleton{\min{σ}{(}{\re} J_(n)(a))}ifnis odd,j=(n+1)/2and|a|>1 , or the empty set∅if otherwise, where, for anyn -by- nmatrixA ,A[j]denotes itsj th principal submatrix obtained by deleting itsj th row andj th column ( 1≤ j≤ n ),\re Aits real part(A+A^(*))/2 , andσ(A)its spectrum. 出版日期： 2013-04-01 資源來源： arXiv.org 版權： http://arxiv.org/licenses/nonexclusive-distrib/1.0 識別號： DOI: 10.48550/arxiv.1304.0295
