Further results on generalized inverses in rings with involution
نویسندگان
چکیده
Let R be a unital ring with an involution. Necessary and sufficient conditions for the existence of the Bott-Duffin inverse of a ∈ R relative to a pair of self-adjoint idempotents (e, f) are derived. The existence of a {1, 3}-inverse, {1, 4}-inverse, and the Moore-Penrose inverse of a matrix product is characterized, and explicit formulas for their computations are obtained. Some applications to block matrices over a ring are given.
منابع مشابه
GENERAL SOLUTIONS TO EQUATION axb ∗ − bx ∗ a ∗ = c IN RINGS WITH INVOLUTION
In [Q. Xu et al., The solutions to some operator equations, Linear Algebra Appl.(2008), doi:10.1016/j.laa.2008.05.034], Xu et al. provided the necessary and sufficient conditions for the existence of a solution to the equation AXB − BXA = C in the general setting of the adjointable operators between Hilbert C-modules. Based on the generalized inverses, they also obtained the general expression ...
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