Timeline for Parametrised Hilbert spaces; can we put a norm on the following space of Hilbert spaces?

11 events

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Jun 14 at 15:02	comment	added	paul garrett		If you do have continuous maps among the $H(s)$'s that fit together well, as @TobiasDiez comments, you do have limits or colimits of the spaces. In fact, in the category of locally convex topological vector spaces, this does (uniquely...) characterized topologies on the (co)limits.
Jan 25, 2014 at 9:36	vote	accept	weasd
Dec 10, 2013 at 15:07	answer	added	User4891		timeline score: 2
Dec 10, 2013 at 14:14	comment	added	weasd		@Tobias Yes that's (continuous maps between the $H(s)$) exactly what I have. I will have a look at the things you mentioned. Thanks.
Dec 10, 2013 at 13:54	comment	added	Tobias Diez		In your problem, do you have an explicit dependence of $\Omega_s$ from $s$ which allows you to define a continuous map from $H(s)$ to $H(s')$ for every $s < s'$ or $s > s'$? In that case you might want to have a look at the inverse and direct limit construction of topological vector spaces. In this way you don't have a topology on $H$ but have nonetheless a limit space $\lim H(s)$.
Dec 10, 2013 at 13:33	answer	added	Liviu Nicolaescu		timeline score: 1
Dec 10, 2013 at 12:17	comment	added	Dan Petersen		Maybe mathoverflow.net/questions/101526 can help.
Dec 10, 2013 at 11:59	review	First posts
Dec 10, 2013 at 12:00
Dec 10, 2013 at 11:57	answer	added	Dirk		timeline score: 1
Dec 10, 2013 at 11:54	history	edited	weasd	CC BY-SA 3.0	added 87 characters in body
Dec 10, 2013 at 11:41	history	asked	weasd	CC BY-SA 3.0