The Gelfand Mazur theorem states that 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
Explore with Wolfram|Alpha
References
Murphy, G. J. C*-Algebras and Operator Theory. New York: Academic Press, 1990.Referenced on Wolfram|Alpha
Gelfand Mazur TheoremCite this as:
Weisstein, Eric W., with contributions by Mohammad Sal Moslehian. "Gelfand Mazur Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GelfandMazurTheorem.html