Talk:Disk algebra

I want to clarify an edit I made. I removed the statement that the disk algebra is a PID because I thought it was misleading without context. An alternative would be to provide the context and state precisely what is meant. Every norm closed ideal in the disk algebra is generated as a norm closed ideal by a single element. But I think that to be worth stating this should be given in the context of a description of the ideals (to be found for example in Chapter 6 of Hoffman's book). I'm not interested in doing this anytime soon. 128.255.45.80 (talk) 05:52, 10 November 2009 (UTC)[reply]

Strange sentence

This article now says the following:

the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions
f : D → C,
where D is the open unit disk in the complex plane C, f extends to a continuous function on the closure of D.

This seems like two sentences separated by a comma. At this point I suspect that what was intended is this:

the disk algebra A(D) (also spelled disc algebra) is the set of holomorphic functions
f : D → C,
where D is the open unit disk in the complex plane C for which f extends to a continuous function on the closure of D.

Is that what is meant?

This could easily be misunderstood as saying the disk algebra is the algebra of holomorphic functions on the open unit disk AND that every such function can be extended to a continuous complex-valued function on the closure. But that is false, as shown by the example ${\textstyle z\mapsto 1/(1-z).}$ Michael Hardy (talk) 11:17, 21 June 2021 (UTC)[reply]