Semi–Fredholm Spectrum and Weyl's Theorem for Operator Matrices

Browder spectra for upper triangular operator matrices

“…In [3], we give the necessary and sufficient condition on A and B such that there exists an operator C for which M C is upper semi-Fredholm. In this section, one of our main results is: …”

“…Let M 0 = A 0 0 B . The upper triangular operator matrices have been studied by many authors (for example [3,4,[7][8][9] etc.). This paper is concerned with the Browder spectrum for 2 × 2 upper triangular operator matrices.…”

The semi-Fredholmness of 2×2 operator matrices

“…One way to study operators is to see them as entries of simpler operators. The operator matrices have been studied by numerous authors [1][2][3][4][5][6][7][8][9][10][11][12][13]. This paper is concerned with the semi-Fredholmness of 2 × 2 operator matrices.…”

On the Right (Left) Invertible Completions for Operator Matrices

“…One way to study operators is to see them as being composed of simpler operators. The operator matrices have been studied by numerous authors [4][5][6]8,9,12,[14][15][16][17][18][19]23,25]. This paper is concerned with the right (left) invertibility of 2 × 2 operator matrices.…”

“…In the case in which C = 0, the invertibility and the left (right) invertibility of M X were characterized in [12] and [17] respectively, and many types of spectra for M X were considered in [4][5][6]8,9,18,19,25]. In the general case, Takahashi [23] had studied the invertibility of M X .…”