On the Maximality
نویسندگان
چکیده
As our proof depends only on the invariant subspace theorem for H1 [2, Theorem 7 ] ; see also [4 ], where Hl denotes the L1 closure of A, and the F. and M. Riesz theorem [3, p. 47], it works in any situation in which these two theorems are valid. Some algebras in which both theorems are valid were considered by Bishop [l]. Even though the proof extracted by Cohen [3, p. 94] from the proof of Wermer's theorem by Hoffman and Singer is at most equally short and certainly more elementary (as it does not use the F. and M. Riesz theorem), our proof seems to be of independent interest because of its generality, and because of the connection it exhibits between the maximality of an algebra and the properties of its annihilating measures. Proof of Wermer's theorem. Let 23 be a proper closed subalgebra of C containing A. We have to show that BÇA, or equivalently
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