Partitions of spectral sets
Peak Points for Algebras on Circled Sets.
Pervasive algebras and maximal subalgebras
A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X). It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive...
Pervasive algebras on planar compacts
We characterize compact sets in the Riemann sphere not separating for which the algebra of all functions continuous on and holomorphic on , restricted to the set , is pervasive on .
Polynomial identification in uniform and operator algebras.
Positive multiplication preserves dissipativity in commutative -algebras.
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
Power boundedness in Banach algebras associated with locally compact groups
Let G be a locally compact group and B(G) the Fourier-Stieltjes algebra of G. Pursuing our investigations of power bounded elements in B(G), we study the extension property for power bounded elements and discuss the structure of closed sets in the coset ring of G which appear as 1-sets of power bounded elements. We also show that L¹-algebras of noncompact motion groups and of noncompact IN-groups with polynomial growth do not share the so-called power boundedness property. Finally, we give a characterization...
Power series developments in lattice ordered semigroups.
Products of n open subsets in the space of continuous functions on [0,1]
Let O₁,...,Oₙ be open sets in C[0,1], the space of real-valued continuous functions on [0,1]. The product O₁ ⋯ Oₙ will in general not be open, and in order to understand when this can happen we study the following problem: given f₁,..., fₙ ∈ C[0,1], when is it true that f₁ ⋯ fₙ lies in the interior of for all ε > 0 ? ( denotes the closed ball with radius ε and centre f.) The main result of this paper is a characterization in terms of the walk t ↦ γ(t): = (f₁(t),..., fₙ(t)) in ℝⁿ. It has to...
Proper uniform algebras are flat
In this brief note, we see that if is a proper uniform algebra on a compact Hausdorff space , then is flat.
Properties of function algebras in terms of their orthogonal measures
In the present note, we characterize the pervasive, analytic, integrity domain and the antisymmetric function algebras respectively, defined on a compact Hausdorff space , in terms of their orthogonal measures on .