Generalized invertibility of operator matrices

Fredholmness and Weylness of block operator matrices

“…For some results in the setting of (separable) Hilbert spaces consult [2], [3], [4], [13], [14], [16], [17], [18], [19], [21], [22], [24]. Results in the setting of Banach spaces can be found in [6], [7], [8], [15], [20], [23], [25], [26]. For some historical remarks in a connection with this topic consult [20].…”

Perturbation of Browder spectrum of upper triangular operator matrices

“…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 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.…”