Advances in Operator Theory
- Adv. Oper. Theory
- Volume 2, Number 3 (2017), 287-292.
Semigroup homomorphisms on matrix algebras
We explore the connection between ring homomorphisms and semigroup homomorphisms on matrix algebras over rings or $C^*$-algebras. Further, we give a connection between group homomorphisms on the general linear groups of a matrix stable $C^*$-algebra and their potentially extended homomorphisms on the whole $C^*$-algebra.
Adv. Oper. Theory, Volume 2, Number 3 (2017), 287-292.
Received: 15 February 2017
Accepted: 26 April 2017
First available in Project Euclid: 4 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 20M25: Semigroup rings, multiplicative semigroups of rings [See also 16S36, 16Y60] 15B33: Matrices over special rings (quaternions, finite fields, etc.)
Burgstaller, Bernhard. Semigroup homomorphisms on matrix algebras. Adv. Oper. Theory 2 (2017), no. 3, 287--292. doi:10.22034/aot.1702-1121. https://projecteuclid.org/euclid.aot/1512431677