Abstract:

According to the characteristics of spectrum of the upper triangular operator matrices on the diagonal and the properties of the diagonal operator matrices corresponding to the upper triangular operator matrices, we investigated the stability of property (ω) for the square of the upper triangular operator matrices under compact perturbation, and gave the sufficient and necessary conditions for the square of the upper triangular operator matrices satisfying the compact perturbation of property (ω).

Key words: upper triangular operator matrix, property (ω), compact perturbation