Geodesic
On a Characterization of Maximal Ideals
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 219-220

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Let A be a commutative complex Banach algebra with identity e. Gleason [1] (cf. also Kahane and Żelazko [2]) has given the following characterization of maximal ideals in A.Theorem. A subspace X ⊂ A of codimension one is a maximal ideal in A if and only if it consists of non-invertible elements.The proofs given by Gleason and by Kahane and Żelazko are both based on the use of Hadamard's factorization theorem for entire functions. In this note we show that this can be avoided by using elementary properties of analytic functions. 
Siddiqi, Jamil A. On a Characterization of Maximal Ideals. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 219-220. doi: 10.4153/CMB-1970-044-6
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     title = {On a {Characterization} of {Maximal} {Ideals}},
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     doi = {10.4153/CMB-1970-044-6},
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