Study on Hirano Invertibility of Two New Types of Perturbed Operator Matrices
Abstract
We investigate the Hirano invertibility of block-operator matrices in Banach algebras, and obtain the Hirano inverse of matrix bmatrix A&B\\ C&D bmatrix under two types of new perturbation conditions. Furthermore, we provide a new operator matrix decomposed into the sum of tripotent and nilpotent elements on Banach spaces.
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