|Title:||On maps preserving zeros of the polynomial xy − yx*||Authors:||Chebotar, Mikhail-A.
|Keywords:||Linear preserver problems;Functional identities;d-Free subsets||Issue Date:||2005||Start page/Pages:||230-243||Source:||Linear Algebra and its Applications 408||Abstract:||
Let A = Mn(F) be the matrix algebra over a field F with an involution, where n≧20.
Suppose that θ : A → A is a bijective linear map such that θ(x)θ(y) = θ(y)θ(x)* for all
x, y ∈ A such that xy = yx*.We show that θ is of the form θ(x) = λuxu−1 for x ∈ A, where
λ is a nonzero symmetric scalar and u is a normal matrix such that uu* is a nonzero scalar.
|Appears in Collections:||數學系|
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