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Similarity preserving linear maps on upper triangular matrix algebras

โœ Scribed by Guoxing Ji; Baowei Wu


Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
160 KB
Volume
414
Category
Article
ISSN
0024-3795

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Let M n be the algebra of all n ร— n complex matrices and P n the set of all idempotents in M n . Suppose ฯ† : M n โ†’ M n is a surjective map satisfying A -ฮปB โˆˆ P n if and only if

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โœ Wai-Leong Chooi; Ming-Huat Lim ๐Ÿ“‚ Article ๐Ÿ“… 2003 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 206 KB

In this article we classify rank-one nonincreasing maps ฯˆ on n-square block triangular matrix algebras with the assumption that ฯˆ(I n ) is of rank n. As applications, we obtain complete classifications of adjugate-commuting maps, and compound-commuting maps on block triangular matrix algebras.