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Additive Maps on Matrix Algebras Preserving Invertibility or Singularity

✍ Scribed by Ajda Fošner; Peter Šemrl


Publisher
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
Year
2005
Tongue
English
Weight
123 KB
Volume
21
Category
Article
ISSN
1439-7617

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Maps on matrix algebras preserving idemp
✍ Gregor Dolinar 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 115 KB

Let M n be the algebra of all n × n complex matrices and P n the set of all idempotents in M n . Suppose φ : M n → M n is a surjective map satisfying A -λB ∈ P n if and only if

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✍ M. Radjabalipour 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 135 KB

Given Hilbert spaces H and K and a von Neumann algebra A ⊂ B(H ), let denote the class of all additive mappings ϕ : The paper shows that if A contains no nonzero abelian central projection then every ϕ ∈ preserves the \* -operation, the R-linear combination, and, up to a commuting operator multiple