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Assume a finite set of functions in , the space of bounded analytic functions on the open unit disc. We give a sufficient condition on a function in to belong to the norm-closure of the ideal generated by , namely the propertyfor some function : satisfying The main feature in the proof is an improvement in the contour-construction appearing in L. Carleson’s solution of the corona-problem. It is also shown that the propertyfor some constant , does not necessary imply that is...
The class ω(A) of ideals consisting of topological zero divisors of a commutative Banach algebra A is studied. We prove that the maximal ideals of the class ω(A) are of codimension one.
Let X be a completely regular topological space and A a commutative locally m-convex algebra. We give a description of all closed and in particular closed maximal ideals of the algebra C(X,A) (= all continuous A-valued functions defined on X). The topology on C(X,A) is defined by a certain family of seminorms. The compact-open topology of C(X,A) is a special case of this topology.
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