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Additive mappings decreasing rank one
Abstract Let B ( X ) be the algebra of bounded operators on a real or complex Banach space X , and F( X ) a subalgebra of finite rank operators. A complete description of additive mappings Φ:F( XExpand
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Mappings that preserve pairs of operators with zero triple Jordan product
Abstract Let F be a field and n ⩾ 3 . Suppose S 1 , S 2 ⊆ M n ( F ) contain all rank-one idempotents. The structure of surjections ϕ : S 1 → S 2 satisfying ABA = 0 ⇔ ϕ ( A ) ϕ ( B ) ϕ ( A ) = 0 isExpand
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Additive mappings on symmetric matrices
Additive mappings, which do not increase the minimal rank of symmetric matrices are classified in characteristic two or three.
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Additive spectrum compressors
Abstract Additive bijections Φ : A → B , which compress the spectrum between two unital, standard operator algebras, are characterized. Applications to local approximate (anti)multiplications areExpand
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Additive idempotence preservers
Abstract Let A be a local matrix algebra over a field of characteristic different from 2, B an arbitrary algebra, and X , Y Banach spaces. Additive mappings Φ: A → B , which preserve idempotents areExpand
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On diameter of the commuting graph of a full matrix algebra over a finite field
TLDR
It is shown that the commuting graph of a matrix algebra over a finite field has diameter at most five if the size of the matrices is not a prime nor a square of a prime. Expand
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Commuting graphs and extremal centralizers
TLDR
We determine the conditions for matrix centralizers which can guarantee the connectedness of the commuting graph for the full matrix algebra M n ( F ) over an arbitrary field F . Expand
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On the gibson barrier for the pólya problem
We study lower bounds on the number of nonzero entries in (0, 1) matrices such that the permanent is always convertible to the determinant by placing ± signs on matrix entries.
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On maximal distances in a commuting graph
We study maximal distances in the commuting graphs of matrix algebras defined over algebraically closed fields. In particular, we show that the maximal distance can be attained only between twoExpand
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Extremal matrix centralizers
Abstract Matrices with maximal or minimal centralizers are classified over fields with sufficiently large orders.
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