### Semigroup homomorphisms on matrix algebras

Bernhard Burgstaller

#### Abstract

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.

#### Article information

Source
Adv. Oper. Theory, Volume 2, Number 3 (2017), 287-292.

Dates
Accepted: 26 April 2017
First available in Project Euclid: 4 December 2017

https://projecteuclid.org/euclid.aot/1512431677

Digital Object Identifier
doi:10.22034/aot.1702-1121

Mathematical Reviews number (MathSciNet)
MR3730055

Zentralblatt MATH identifier
1383.46038

#### Citation

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

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