Tensor product of URM algbras
The Banach algebra of continuous bounded functions with separable support
We prove a commutative Gelfand-Naimark type theorem, by showing that the set of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space X (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to C₀(Y) for some unique (up to homeomorphism) locally compact Hausdorff space Y. The space Y, which we explicitly construct as a subspace of the Stone-Čech compactification of X, is countably compact, and if X is non-separable,...
The characteristic algebra of a polynomial covering map.
The Complex Stone-Weierstrass Property
The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,ℂ) which separates points and contains the constant functions is dense in C(X,ℂ). Results of W. Rudin (1956) and Hoffman and Singer (1960) show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some general facts about the CSWP; in particular we show that if X is a compact ordered space,...
The fixed point property of unital abelian Banach algebras.
The Fourier algebra of SL(2,...)......, n...2, has no multiplier bounded approximate unit.
The Pełczyński property for some uniform algebras
The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras.
The Uniform Algebra Generated by z and a Smooth Even Function.
The weak Phillips property
Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
Theorems of Korovkin type for adapted spaces
It is shown that the methods developed in an earlier paper of the author about a Dirichlet problem for the Silov boundary [Annales Inst. Fourier, 11 (1961)] lead in a new and natural way to the most important results about the convergence of positive linear operators on spaces of continuous functions defined on a compact space. Choquet’s notion of an adapted space of continuous functions in connection with results of Mokobodzki-Sibony opens the possibility of extending these results to the case...
Toeplitz operators for hypodirichlet algebras
Topological Algebras of Functions of Bounded Variation I.
Topological Algebras of Functions of Bounded Variation II.
Topologies on the Extreme Points of Compact Convex Sets II.
Translation-invariant function algebras on compact abelian groups.
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.