Moore–Penrose inverse in rings with involution

By Jerry J. Koliha, Dragan S. Djordjevi'c, Dragana S. Cvetković. 2007

147 citations recorded by the source corpus.

Abstract We study the Moore–Penrose inverse (MP-inverse) in the setting of rings with involution. The results include the relation between regular, MP-invertible 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/82dfc773c81d6b4ae84dc90f43f5ca69ea051a95

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In Algebra and Number Theory

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Citations in the corpus

REVERSE ORDER LAW FOR THE MOORE-PENROSE INVERSE OF CLOSED-RANGE ADJOINTABLE OPERATORS ON HILBERT C*-MODULES (2014, background): “See also [5] and [11] for some algebraic aspects.”
EP elements in rings (2009, unknown): “There is at most one b such that above conditions hold (see [6, 12, 14, 16]).”
Characterizations of core and dual core inverses in rings with involution (2016, background): “In [8], Xu and Chen gave the characterizations and expressions of Moore–Penrose inverse of an element by a Hermitian element (or a projection).”
Moore–Penrose-invertible normal and Hermitian elements in rings (2009, unknown): “Then a is group invertible if there is a# ∈ R such that aaa = a, aaa = a, aa = aa; a# is a group inverse of a and it is uniquely determined by these equations [4].”
Group, Moore–Penrose, core and dual core inverse in rings with involution☆ (2014, background): “Some characterizations of the MP invertibility of an element of a ring is given in [8].”