If 
is a unital Banach algebra where every nonzero element is invertible, then 
is the algebra of complex numbers.
Gelfand Mazur Theorem
This entry contributed by Mohammad Sal Moslehian
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References
Murphy, G. J. C-*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Gelfand Mazur TheoremCite this as:
Moslehian, Mohammad Sal. "Gelfand Mazur Theorem." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/GelfandMazurTheorem.html