Talk:Banach function algebra

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Stub-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Stub Class
Low Importance
 Field:  Analysis

The article as is doesn't shed much light on much. We need expansions and examples here. Some questions to answer when someone knowledgeable gets to edits this:

  • Is closedness not required in the definition?
  • What is the relationship between characters on A, the space X, and the "support" of A?
  • Give some examples. Take C(X), X compact Hausdorff. Take a closed *-ideal corresponding to some closed set of X. Forget the C*-structure, so we have a Banach function algebra. What is the character space? Is it the obvious guess, the quotient space?
  • How about examples different from above? Take, for instance, analytic polynomials on the circle, what is the character space? Presumably this is bigger than the circle and related to the Shilov boundary somehow? Mct mht (talk) 00:16, 1 June 2012 (UTC)