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http://dx.doi.org/10.4134/JKMS.j190306

WEIGHTED MOORE-PENROSE INVERSES OF ADJOINTABLE OPERATORS ON INDEFINITE INNER-PRODUCT SPACES  

Qin, Mengjie (Department of Mathematics Shanghai Normal University)
Xu, Qingxiang (Department of Mathematics Shanghai Normal University)
Zamani, Ali (Department of Mathematics Farhangian University)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.3, 2020 , pp. 691-706 More about this Journal
Abstract
Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A†MN exists, where A is an adjointable operator between Hilbert C⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A†MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.
Keywords
Hilbert $C^{\ast}$-module; weighted Moore-Penrose inverse; indefinite inner-product space;
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