Can I read A Normal Uniform Algebra That Fails to Be Strongly Regular at a Peak Point on EtoBox?

A Normal Uniform Algebra That Fails to Be Strongly Regular at a Peak Point by Izzo, Alexander J. is a scholarly article available to read on EtoBox.

What is A Normal Uniform Algebra That Fails to Be Strongly Regular at a Peak Point about?

It is shown that there exists a normal uniform algebra, on a compact metrizable space, that fails to be strongly regular at some peak point. This answers a 31-year-old question of Joel Feinstein. Our example is R(K) for a certain compact planar set K. Furthermore, it has a totally ordered one-parameter family of closed primary ideals whose hull is a peak point. General results regarding lifting ideals under Cole root extensions are established. These results are applied to obtain a normal uniform algebra, on a compact metrizable space, with every point a peak point but again having a totally ordered one-parameter family of closed primary ideals.

Author

Izzo, Alexander J.

Published

2023

Language

EN