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On finitely generated closed ideals in H ( D )

Jean Bourgain (1985)

Annales de l'institut Fourier

Assume f 1 , ... , f N a finite set of functions in H ( D ) , the space of bounded analytic functions on the open unit disc. We give a sufficient condition on a function f in H ( D ) to belong to the norm-closure of the ideal I ( f 1 , ... , f N ) generated by f 1 , ... , f N , namely the property | f ( z ) | α ( | f 1 ( z ) | + ... + | f N ( z ) | ) for z D for some function α : R + R + satisfying lim t 0 α ( t ) / t = 0 . 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 property | f ( z ) | C max 1 j N | f j ( z ) | for z D for some constant C , does not necessary imply that f is...

On ideals consisting of topological zero divisors

Antoni Wawrzyńczyk (2000)

Studia Mathematica

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.

On the ideal structure of algebras of LMC-algebra valued functions

Jorma Arhippainen (1992)

Studia Mathematica

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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