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Ring homomorphisms on real Banach algebras. (English) Zbl 1038.46042

Summary: Let \(B\) be a strictly real commutative real Banach algebra with the carrier space \(\Phi_{B}\). If \(A\) is a commutative real Banach algebra, then we give a representation of a ring homomorphism \(\rho : A \rightarrow B\) which need not be linear nor continuous. If \(A\) is a commutative complex Banach algebra, then \(\rho(A)\) is contained in the radical of \(B\).

MSC:

46J05 General theory of commutative topological algebras
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