Abstract and Applied Analysis

Linear Maps on Upper Triangular Matrices Spaces Preserving Idempotent Tensor Products

Li Yang, Wei Zhang, and Jinli Xu

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Abstract

Suppose m , n 2 are positive integers. Let 𝒯 n be the space of all n × n complex upper triangular matrices, and let ϕ be an injective linear map on 𝒯 m 𝒯 n . Then ϕ ( A B ) is an idempotent matrix in 𝒯 m 𝒯 n whenever A B is an idempotent matrix in 𝒯 m 𝒯 n if and only if there exists an invertible matrix P 𝒯 m 𝒯 n such that ϕ ( A B ) = P ( ξ 1 ( A ) ξ 2 ( B ) ) P - 1 ,   ∀ A 𝒯 m ,   B 𝒯 n , or when m = n , ϕ ( A B ) = P ( ξ 1 ( B ) ξ 2 ( A ) ) P - 1 ,   ∀ A 𝒯 m ,   B 𝒯 m , where ξ 1 ( [ a i j ] ) = [ a i j ] or ξ 1 ( [ a i j ] ) = [ a m - i + 1 , m - j + 1 ] and ξ 2 ( [ b i j ] ) = [ b i j ] or ξ 2 ( [ b i j ] ) = [ b n - i + 1 , n - j + 1 ] .

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 148321, 8 pages.

Dates
First available in Project Euclid: 26 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1395857995

Digital Object Identifier
doi:10.1155/2014/148321

Mathematical Reviews number (MathSciNet)
MR3166569

Zentralblatt MATH identifier
1142.11027

Citation

Yang, Li; Zhang, Wei; Xu, Jinli. Linear Maps on Upper Triangular Matrices Spaces Preserving Idempotent Tensor Products. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 148321, 8 pages. doi:10.1155/2014/148321. https://projecteuclid.org/euclid.aaa/1395857995


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