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The Bourgain algebra of the disk algebra A(𝔻) and the algebra QA

Joseph CimaRaymond Mortini — 1995

Studia Mathematica

It is shown that the Bourgain algebra A ( ) b of the disk algebra A() with respect to H ( ) is the algebra generated by the Blaschke products having only a finite number of singularities. It is also proved that, with respect to H ( ) , the algebra QA of bounded analytic functions of vanishing mean oscillation is invariant under the Bourgain map as is A ( ) b .

Simultaneous stabilization in A ( )

Raymond MortiniBrett D. Wick — 2009

Studia Mathematica

We study the problem of simultaneous stabilization for the algebra A ( ) . Invertible pairs ( f j , g j ) , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that α f j + β g j 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 A ( ) has stable rank two, we are faced here with a different situation....

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