亚正规算子之间的距离

Distance between Hyponormal Operators

利用算子的谱给出两个亚正规算子间距离上限的刻画,并对亚正规算子A,得出inf‖A-λI‖=‖A‖λ∈C当且仅当∩ U(x,‖A‖)={0} x∈σ(A),其中U(x,‖A‖)={z∈C;|z-x|≤‖A‖}.

An upper bound is obtained for the distance between two hyponormal operators in terms of the distance between their spectra. Moreover, for a hyponormal operator A, the condition inf λ∈C‖A-λI‖=‖A‖is equivalent to ∩x∈σ（A）U（x,‖A‖）={0},where U（x,‖A‖）={z∈C;｜z-x｜≤‖A‖}.