• Corpus ID: 254044212

A sharper Swiss cheese

  title={A sharper Swiss cheese},
  author={Alexander J. Izzo},
. It is shown that there exists a compact planar set K such that the uniform algebra R ( K ) is nontrivial and strongly regular. This answers a 53-year-old question of Donald Wilken. Dedicated to the memory of Harold Garth Dales 



A general method for constructing essential uniform algebras

A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform

Uniform Algebras

Given a variety of algebras V, we study categories of algebras in V with a compatible structure of uniform space. The lattice of compatible uniformities of an algebra, Unif A, can be considered a

S-Algebras on Sets in C n

We give conditions which are necessary and sufficient for polynomial approximation of any continuous function on a compact subset of Cn. Let X be a compact set in Cn, complex n-space, P(X) the

Bounded point derivations on certain Banach algebras

A Note on Strongly Regular Function Algebras

  • D. Wilken
  • Mathematics
    Canadian Journal of Mathematics
  • 1969
Let A be a uniformly closed subalgebra of C(X), the algebra of all complex-valued continuous functions on a compact Hausdorff space X. If A separates the points of X and contains the constant

A nontrivial normal sup norm algebra

5. , Markoff chains and Martin boundaries, Illinois J. Math. 4 (I960), 313340. 6. R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49(1941), 137-172. 7. P. A. Meyer,

Banach algebras and automatic continuity

Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination. This volume expounds the general theory of Banach algebras,

A cheaper Swiss cheese