Topological Algebras with Finitely-Generated Bases.
Topological algebras with maximal regular ideals closed
It is shown that all maximal regular ideals in a Hausdorff topological algebra A are closed if the von Neumann bornology of A has a pseudo-basis which consists of idempotent and completant absolutely pseudoconvex sets. Moreover, all ideals in a unital commutative sequentially Mackey complete Hausdorff topological algebra A with jointly continuous multiplication and bounded elements are closed if the von Neumann bornology of A is idempotently pseudoconvex.
Topologies et compactologies
Topologies on the Extreme Points of Compact Convex Sets II.
Topologies on the space of ideals of a Banach algebra
Some topologies on the space Id(A) of two-sided and closed ideals of a Banach algebra are introduced and investigated. One of the topologies, namely , coincides with the so-called strong topology if A is a C*-algebra. We prove that for a separable Banach algebra coincides with a weaker topology when restricted to the space Min-Primal(A) of minimal closed primal ideals and that Min-Primal(A) is a Polish space if is Hausdorff; this generalizes results from [1] and [5]. All subspaces of Id(A)...
Translation-invariant function algebras on compact abelian groups.
Translations of functions iv vector Hardy classes on the unit disk [Book]
Trivial generators for nontrivial fibres
Pseudoconvex domains are exhausted in such a way that we keep a part of the boundary fixed in all the domains of the exhaustion. This is used to solve a problem concerning whether the generators for the ideal of either the holomorphic functions continuous up to the boundary or the bounded holomorphic functions, vanishing at a point in where the fibre is nontrivial, has to exceed . This is shown not to be the case.
Trivial Jensen measures without regularity
In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point.
Truncated Toeplitz Operators on the Polydisk.
Two observations on a theorem by Coifman