Finitely Generated Prime Ideals in H? and A (ID).
Die Potenzreihe ... .
A constructive proof of the Beurling-Rudin theorem
A constructive proof of the Beurling-Rudin theorem on the characterization of the closed ideals in the disk algebra A(𝔻) is given.
An example of a subalgebra of on the unit disk whose stable rank is not finite
We present an example of a subalgebra with infinite stable rank in the algebra of all bounded analytic functions in the unit disk.
Embedding polydisk algebras into the disk algebra and an application to stable ranks
It is shown how to embed the polydisk algebras (finite and infinite ones) into the disk algebra A(𝔻̅). As a consequence, one obtains uniform closed subalgebras of A(𝔻̅) which have arbitrarily prescribed stable ranks.
The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem
Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's theorem the Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.
The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA
It is shown that the Bourgain algebra of the disk algebra A() with respect to is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is .
An upper bound for the distance to finitely generated ideals in Douglas algebras
Let f be a function in the Douglas algebra A and let I be a finitely generated ideal in A. We give an estimate for the distance from f to I that allows us to generalize a result obtained by Bourgain for to arbitrary Douglas algebras.
Simultaneous stabilization in
We study the problem of simultaneous stabilization for the algebra . Invertible pairs , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since has stable rank two, we are faced here with a different situation....
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