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

On functional representation of locally $m$ -pseudoconvex algebras.

Arhippainen, Jorma (1999)

International Journal of Mathematics and Mathematical Sciences

On Global Central Decomposition for a Universal Cap.

C.M. Edwards (1975)

Mathematische Annalen

On ideal of joint topological divisors of zero

L. Lindahl (1975)

Studia Mathematica

On ideals consisting of joint topological divisors of zero

Zbigniew Słodkowski (1973)

Studia Mathematica

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 Integral Representation and the Choquet Boundary for Convolution Algebras of Measures.

Gunter Ritter, Susanna Papadopoulou (1982)

Monatshefte für Mathematik

On Liouville F-Algebras

John Daly (1971)

Studia Mathematica

On maximal ideals in commutative m-convex algebras

W. Żelazko (1976)

Studia Mathematica

On non-removable ideals in commutative locally convex algebras

W. Żelazko (1983)

Studia Mathematica

On permanent radicals in commutative locally convex algebras

W. Żelazko (1983)

Studia Mathematica

On ring derivations and quadratic functionals.

Peter Semrl (1991)

Aequationes mathematicae

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.

On the ideal structure of commutative Banach algebras

Yngve Domar (1982)

Banach Center Publications

On The Symmetric Quaternionic Banach Algebras, I (Geljfand Theory)

Aleksandar Torgašev (1978)

Publications de l'Institut Mathématique

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