算子代数上保持升降标的线性映射

Linear maps betw een operator algebras preserving the ascent and descent

设B(H)为无限维可分的复Hilbert空间H上的有界线性算子的全体,φ为B(H)上满的线性映射。若φ保持上半Browder谱或降标谱并且保持孤立点集,则φ为B(H)上的自同构。当φ保持Drazin谱并且保持孤立点集时,刻画了线性映射φ的两种可能结构。

Let B（ H） be the algebra of all bounded linear operators on infinite dimensional complex Hilbert space H, and letφ：B（ H）→B（ H） be a surjective linear map.Ifφpreserves the upper semi-Browder spectrum or descent spec-trum and the set of isolated points, thenφis an automorphism on B（ H） .Ifφpreserves the Drazin spectrum and the set of isolated points, the φtwo probable structures are given.