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Linear Maps Preserving Generalized Invertibility

✍ Scribed by Mostafa Mbekhta; Leiba Rodman; Peter Šemrl


Publisher
SP Birkhäuser Verlag Basel
Year
2006
Tongue
English
Weight
210 KB
Volume
55
Category
Article
ISSN
0378-620X

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📜 SIMILAR VOLUMES


On invertibility preserving linear mappi
✍ Erik Christensen 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 133 KB

Let A be a unital matrix algebra, ϕ : A → M n (C) a unital linear mapping and B the algebra generated by ϕ(A). The mapping ϕ is a homomorphism modulo the Jacobson radical in B if and only if for k = dim(B)dim(ϕ(A)) + 3 the mapping ϕ ⊗ id : A ⊗ M k (C) → B ⊗ M k (C) preserves invertibility. This resu