Continuity of ring homomorphisms for local $C^\star$-algebras

I. N. Maliev^a, M. A. Pliev<sup>b

a</sup> North Osetian State University, Vladikavkaz, Russia
^b Southern Mathematical Institute of Russian Academy of Sciences, Vladikavkaz, Russia

Abstract: We show that a ring homomorphism from a local $\sigma-C^\star$-algebra to a local $C^\star$-algebra is a continuous mapping.

Keywords: local $C^\star$-algebras, homomorphisms, positive operators.

UDC: 517.98+519.46

Received: 28.04.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:8, 28–32

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