Hirano Inverse of Anti-triangular Operator Matrix in Banach Algebras
This paper investigated Hirano inverse of anti-triangular operator matrix in Banach algebra.Let a∈AH,b∈AsD.Assuming that bDa=0,babπ=0,it was proven that [ab10] had Hirano inverse.Moreover,Hirano inverse of anti-triangular operator matrix under certain weak commutative conditions was studied.These results provided a new kind of operator matrix with tripotent and nilpotent decompositions.
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