Theoretical study demonstrates explicit representations for generalized core-EP inverses in anti-triangular operator matrices, indicating new pathways to solve 2x2 block operators.
In this paper, we derive explicit formulae for the generalized core-EP inverse of a anti-triangular operator matrix via two distinct and novel approaches. Furthermore, by exploiting these new structural insights, we extend the application to establish the core and core-EP inverses for some 2× 2 block operator matrices.
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Huanyin Chen (2026) studied this question.
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