Elements of C*-algebras commuting with their Moore-Penrose inverse
نویسندگان
چکیده
منابع مشابه
Moore–Penrose inverse in rings with involution
We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MPinvertible and well-supported elements. We present an algebraic proof of the reverse order rule for the MP-inverse valid under certain conditions on MP-invertible elements. Applications to C∗-algebras are given. 2000 Mathematics Subject Classification: 46L...
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In this paper, several equivalent conditions related to the reverse order law for the Moore-Penrose inverse in C-algebras are studied. Some well-known results are extended to more general settings. Then this result is applied to obtain the reverse order rule for the weighted Moore-Penrose inverse in C-algebras.
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Let Qk,n = {α = (α1, · · · , αk) : 1 ≤ α1 < · · · < αk ≤ n} denote the strictly increasing sequences of k elements from 1, . . . , n. For α, β ∈ Qk,n we denote by A[α, β] the submatrix of A with rows indexed by α, columns by β. The submatrix obtained by deleting the α-rows and β-columns is denoted by A[α′, β′]. For nonsingular A ∈ IRn×n, the Jacobi identity relates the minors of the inverse A−1...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2000
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-139-1-81-90