Timeline for Is the space $S'(\mathbb{N})$ of slowly increasing sequences the projective limit of Hilbert sequence spaces?

Current License: CC BY-SA 3.0

13 events

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Jun 15, 2020 at 7:27	history	edited	CommunityBot		Commonmark migration
Oct 13, 2016 at 5:43	history	edited	Goulifet	CC BY-SA 3.0	added 19 characters in body
Feb 10, 2015 at 13:40	vote	accept	Goulifet
Feb 10, 2015 at 13:39	answer	added	Goulifet		timeline score: 5
Jan 28, 2015 at 16:18	history	edited	Goulifet	CC BY-SA 3.0	deleted 1 character in body
Jan 28, 2015 at 16:15	comment	added	Goulifet		@weather thank you for you answer. If I understand correctly, from Köthe, we can define on $S'(\mathbb{N})$ a family of semi-norms $p_{u}(v) = \sum \|u_i\|\|v_i\|$ with $u\in S(\mathbb{N})$. I interpret this saying that $S'(\mathbb{N})$ is an intersection of weighted $\ell_1$ spaces (with weights in the space $S(\mathbb{N})$). Also, can I extract a countable family from these weights? This is not clear to me.
Jan 27, 2015 at 17:06	history	edited	Goulifet	CC BY-SA 3.0	added 28 characters in body
Jan 27, 2015 at 16:56	comment	added	weather		I assume that you are missing an intersection sign in the second bottom line. The answer to your question is yes, by the way---follows from the fact that your spaces are mutually $\alpha$-duals (see Köthe, Garling).
Jan 27, 2015 at 14:17	comment	added	Goulifet		That's true, I did the modification. Thanks.
Jan 27, 2015 at 14:16	history	edited	Goulifet	CC BY-SA 3.0	deleted 1 character in body
Jan 27, 2015 at 13:59	comment	added	Neil Strickland		I think that the definition should be that $u\in\ell_2^m(\mathbb{N})$ if $(u_n(n+1)^m)_{n\in\mathbb{N}}$ lies in $\ell_2(\mathbb{N})$ (not $\ell_2^m(\mathbb{N})$).
Jan 27, 2015 at 13:31	comment	added	David Roberts♦		Your definition of $\ell^m_2(\mathbb{N})$ is confusing...
Jan 27, 2015 at 13:10	history	asked	Goulifet	CC BY-SA 3.0