https://scholars.lib.ntu.edu.tw/handle/123456789/30235
Title: | On maps preserving zeros of the polynomial xy − yx* | Authors: | Chebotar, Mikhail-A. Fong, Yuen Lee, Pjek-Hwee |
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. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/2006111501244176 | Other Identifiers: | 246246/2006111501244176 |
Appears in Collections: | 數學系 |
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