Results 191 to 200 of about 1,103 (233)
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Additive mappings preserving commutativity
Linear and Multilinear Algebra, 1997The general form of additive surjective mappings on Mn which preserve commutativity in both directions is given.
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Additive Maps Preserving Local Spectrum
Integral Equations and Operator Theory, 2005Let X be a complex Banach space, and let \(\mathcal{L}(X)\) be the space of bounded operators on X. Given \(T \in \mathcal{L}(X)\) and x ∈ X, denote by σT (x) the local spectrum of T at x.
Abdellatif Bourhim, Thomas Ransford
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Additive Maps Preserving Nilpotent Perturbation of Scalars
Acta Mathematica Sinica, English Series, 2018Let X be a Banach space over $$\mathbb{F} (=\mathbb{R} \rm{or} \mathbb{C})$$ with dimension greater than 2. Let $$\mathcal{N}(X)$$
Zhang, Ting, Hou, Jin Chuan
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Additive Mappings Preserving Rank–one Idempotents
Acta Mathematica Sinica, English Series, 2005This paper presents a remarkable contribution to the study of additive preservers. It is well-known that the different kinds of rank-one preservers play important roles in the solution of many preserver problems. In the paper under review, the author deals with additive maps preserving idempotents of rank at most one.
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Additive operators preserving rank-additivity on symmetry matrix spaces
Journal of Applied Mathematics and Computing, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tang, Xiao-Min, Cao, Chong-Guang
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Additive preservers on Banach algebras
Publicationes Mathematicae Debrecen, 2003Summary: It is shown that an additive, surjective mapping \(\Phi:\text{soc}({\mathcal A})\to\text{soc}({\mathcal A})\), preserving rank-one idempotents and their linear spans in both directions, is a real-linear Jordan isomorphism provided that \(\mathcal A\) is a semiprime Banach algebra with no nonzero central elements in its socle.
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Sparse Distance Preservers and Additive Spanners
SIAM Journal on Discrete Mathematics, 2005For an unweighted graph $G = (V,E)$, $G' = (V,E')$ is a subgraph if $E' \subseteq E$, and $G'' = (V'',E'',\omega)$ is a Steiner graph if $V \subseteq V''$, and for any pair of vertices $u,w \in V$, the distance between them in $G''$ (denoted $d_{G''}(u,w)$) is at least the distance between them in $G$ (denoted $d_G(u,w)$).
Béla Bollobás +2 more
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Additive maps preserving operator–eigenvector relations
Linear and Multilinear Algebra, 2013Let be a division ring with and , where , for some positive integer . A vector is called an eigenvector of if there exists such that . In this paper, we characterize the additive map such that every eigenvector of is again an eigenvector of for all .
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