Continuous spectrum, point spectrum and residual spectrum of operator matrices

The residual spectrum and the continuous spectrum of upper triangular operator matrices

“…σ(M C ) was determined in [4]. For the approximate point spectrum, the essential spectrum, the Weyl spectrum, the point spectrum, the continuous spectrum and the residual spectrum of M C , analogous results have been obtained in many literatures (see [1,2,5,10]). The sets ∪…”

“…One way to study operators is to see them as being composed of simpler operators. The operator matrices have been studied by numerous authors [1][2][3][4][5][7][8][9][10][11]. This paper is concerned with the residual spectrum and the continuous spectrum of operator matrices.…”

The point spectrum and residual spectrum of upper triangular operator matrices

“…See, e.g., [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In [5,6,9,10,12,[14][15][16][17][18], the perturbations of different spectra (the spectra, left (right) spectra, point spectra, continuous spectra, residual spectra,• • • ) of M X were discussed. In [14,15], the sets…”

Perturbation of Browder spectrum of upper triangular operator matrices

“…The goal of this paper is to present some necessary and sufficient conditions for M C to be Browder for some C ∈ B(Y, X) by using an alternative approach based on matrix representation of operators and the ghost index theorem. Moreover, in the Hilbert space case the characterizations of the Fredholm and invertible perturbations of Browder spectrum are also given.Keywords: operator matrices, Browder spectrum, left semi-Browder spectrum.which motivated the interest in 2 × 2 upper-triangular operator matrices (see [1][2][3][4][5][6][7][8][9][11][12][13][14][15][16][17][18][19][20]). The problems related to the perturbation of spectra of 2-by-2 upper triangular operator matrices were first studied by H. K. Du and J. Pan in [5], and they given the characterization of M C to be invertible for some C ∈ B(K, H) in the Hilbert spece case.…”