ABSTRACT. If every prime ideal is closed in a commutative semiprime Banach algebra with unit, then every derivation on it is continuous.Also if derivations are continuous on integral domains, then they are continuous on semiprime Banach algebras.
ABSTRACT. If every prime ideal is closed in a commutative semiprime Banach algebra with unit, then every derivation on it is continuous.Also if derivations are continuous on integral domains, then they are continuous on semiprime Banach algebras.
ABSTRACT. We characterize all closed subspaces of finite codimension in some specific types of function algebras e.g. these include C(X): algebra of continous functions on a compact Hausdorff space, Cn [a, b]: the algebra of n-times continuously differentiable functions on the closed interval [a, b]. Our work is a generalization of the well-known Gleason-Kahane-Zelazko theorem [3,6] for subspaces of codimension one in arbitrary unitary Banach algebras.
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