On maps preserving zeros of the polynomial xy − yx*
Resource
Linear Algebra and its Applications 408,230-243
Journal
Linear Algebra and its Applications 408
Pages
230-243
Date Issued
2005
Date
2005
Author(s)
Chebotar, Mikhail-A.
Fong, Yuen
Lee, Pjek-Hwee
DOI
246246/2006111501244176
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.
Subjects
Linear preserver problems
Functional identities
d-Free subsets
Type
journal article
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