Representations for weighted Moore-Penrose inverses of partitioned adjointable operators

2010/08/04 by Qingxiang Xu, Xu, Qingxiang, Yonghao Chen +3
Computer Science · Mathematics · #15A09 #46L08 #FOS: Mathematics #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1008.0887

openalex publication_date 2010/08/04 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

For two positive definite adjointable operators M and N, and an adjointable operator A acting on a Hilbert C^*-module, some properties of the weighted Moore-Penrose inverse A^†_MN are established. When A=(A_ij) is 1× 2 or 2× 2 partitioned, general representations for A^†_MN in terms of the individual blocks A_ij are studied. In case A is 1× 2 partitioned, a unified representation for A^†_MN is presented. In the 2× 2 partitioned case, an approach to constructing Moore-Penrose inverses from the non-weighted case to the weighted case is provided. Some results known for matrices are generalized in the general setting of Hilbert C^*-module operators.

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