Properties of the combinations of commutative idempotents
Copyright policy )Properties of the combinations of commutative idempotents
An operator \(T\in B(H)\) is called idempotent if \(T^2=T\). The linear combinations of idempotents have been investigated for many years, see, for instance, \textit{J. Benítez}, \textit{X.-J. Liu} and \textit{T.-P. Zhu} [Linear Multilinear Algebra 58, No.~7--8, 1023--1035 (2010; Zbl 1204.15009)] and references therein. The purpose of the present paper is to characterize the invertibility, the group invertibility and idempotency of the linear combinations of idempotents and their products under certain commutativity properties imposed on idempotents.
- University of Niš Serbia
- South China Normal University China (People's Republic of)
- Fudan University China (People's Republic of)
Numerical Analysis, \(n\)-potent operator, Algebra and Number Theory, linear combination of idempotents, inverse, idempotent, General (adjoints, conjugates, products, inverses, domains, ranges, etc.), group inverse, Linear combination of idempotents, Group inverse, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Geometry and Topology, Inverse
Numerical Analysis, \(n\)-potent operator, Algebra and Number Theory, linear combination of idempotents, inverse, idempotent, General (adjoints, conjugates, products, inverses, domains, ranges, etc.), group inverse, Linear combination of idempotents, Group inverse, Discrete Mathematics and Combinatorics, Theory of matrix inversion and generalized inverses, Geometry and Topology, Inverse
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