Geodesic
On the non-existence of norms for some algebras of functions
Studia Mathematica, Tome 111 (1994) no. 1, pp. 97-101
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Let C(Ω) be the algebra of all complex-valued continuous functions on a topological space Ω where C(Ω) contains unbounded functions. First it is shown that C(Ω) cannot have a Banach algebra norm. Then it is shown that, for certain Ω, C(Ω) cannot possess an (incomplete) normed algebra norm. In particular, this is so for $Ω = ℝ^n$ where ℝ is the reals. 
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Bertram Yood. On the non-existence of norms for some algebras of functions. Studia Mathematica, Tome 111 (1994) no. 1, pp. 97-101. doi: 10.4064/sm-111-1-97-101

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