关键词: 拟-*-A(n)算子, 拟相似, 单值扩展性质, Weyl谱, 本质近似点谱

Abstract:

Let T ∈B(H) be a bounded linear operator on a complex Hilbert space H. In this paper the authors introduce a new class of operator--quasi-*-A(n) and prove some properties of these operators, such as, if T is quasi-*-A(n), then its point spectrum and joint point spectrum are identical. Using these results, the authors also prove that if T or T^* is quasi-*-A(n), then the spectral mapping theorem holds for the weyl spectrum and for the essential approximate point spectrum.

Key words: Quasi-*-A(n), Quasisimilarity, Single valued extension property, Weyl spectrum, Essential approximate point spectrum