The study establishes new representations of the generalized Drazin inverse in Banach algebras, suggesting novel applications for anti-triangular matrices.
We provide representations for the generalized Drazin inverse of an anti-triangular matrix of the form a {pmatrix}a & b \\1 & 0{pmatrix} in a Banach algebra A with commuting elements a, b ? A. In particular, a new formula for the Drazin inverse of an anti-triangular matrix is established by employing Catalan numbers.
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Huanyin Chen (2025) studied this question.
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