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A note on the Gelfand-Mazur Theorem

Authors: S. J. Bhatt, D. J. Karia, S. H. Kulkarni and M. E. Shimpi
Journal: Proc. Amer. Math. Soc. 126 (1998), 2999-3005
MSC (1991): Primary 46K15, 46H20
MathSciNet review: 1476120
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Abstract: Three Gelfand-Mazur type theorems are proved. One of these provides a $C^*$-property analogue of Zalar's recent generalizations of the Froelich-Ingelstam-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.

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S. J. Bhatt
Affiliation: Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar-388 120, Gujarat, India

S. H. Kulkarni
Affiliation: Department of Mathematics, Indian Institute of Technology, Madras, 600 036, India

M. E. Shimpi
Affiliation: Department of Mathematics, BVM Engineering College, Vallabh Vidyanagar-388 120, Gujarat, India

Keywords: Real *-algebra, Pythagorean norm, Gelfand-Mazur Theorem, Froelich-Ingelstam-Smiley Theorem
Received by editor(s): September 23, 1996
Received by editor(s) in revised form: March 12, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society