A note on the Gelfand-Mazur Theorem

Abstract

Abstract. Three Gelfand-Mazur type theorems are proved. One of these provides a C * -property analogue of Zalar's recent generalizations of the FroelichIngelstam-Smiley Theorems concerning unital multiplication in Hilbert spaces; the second illustrates that the assumption in Kaplansky's version of the Gelfand-Mazur Theorem can be weakened in the presence of a C * -norm; whereas the third provides a real analogue of a result due to Srinivasan.