Timeline for When is $A : C(X) \to C(Y)$ a composition operator?

Current License: CC BY-SA 3.0

12 events

when toggle format	what		by	license	comment
S Feb 28, 2018 at 13:32	history	suggested	Evgeny Kuznetsov	CC BY-SA 3.0	Texify a Title
Feb 28, 2018 at 13:06	review	Suggested edits
S Feb 28, 2018 at 13:32
Dec 4, 2009 at 20:44	answer	added	Oleg Eroshkin		timeline score: 4
Dec 4, 2009 at 20:07	history	edited	santker heboln		edited tags
Dec 4, 2009 at 9:00	answer	added	Matthew Daws		timeline score: 0
Dec 3, 2009 at 8:21	history	edited	Andrew Stacey	CC BY-SA 2.5	Converted maths to jsMath, two minor grammatical corrections
Dec 3, 2009 at 3:18	comment	added	Yemon Choi		Seeing as my general topology is, despite Kelley's injunction, pretty shoddy - what exactly is the interest in the particular hypotheses you've chosen? For instance, is it the case that these conditions (hemicompact k-space) are the weakest which allow one to detect properties of the space X from the algebra C_R(X), in some sense? Or are you just choosing some general conditions because they seem interesting to you?
Dec 2, 2009 at 21:12	answer	added	Greg Kuperberg		timeline score: 3
Dec 2, 2009 at 20:51	history	edited	santker heboln	CC BY-SA 2.5	added 555 characters in body
Dec 2, 2009 at 20:05	comment	added	Matthew Daws		You must have missed something out: as written, couldn't I pick some (real-valued) measure $\mu$ on X and define $A:C(X)\rightarrow C(Y)$ by $A(f) = \mu(f) 1$. Then $A(\overline{f}) = \overline{A(f)}$ but $A$ would only be induced by a composition operator if $\mu$ were a point mass at $x_0$, with $T(y)=x_0$ for all $y\in Y$. If $A$ is also a homomorphism, then it's fine (and, AFAIK, you don't actually need it to be a $*$-homomorphism...) What is a hemicompact k-space?
Dec 2, 2009 at 17:32	comment	added	Qiaochu Yuan		You should probably define all of your terms.
Dec 2, 2009 at 17:28	history	asked	santker heboln	CC BY-SA 2.5