Timeline for Is the space of vectorial functions that are Dunford integrable complete?

8 events

when toggle format	what		by	license	comment
Aug 14, 2015 at 11:02	history	edited	Tomasz Kania	CC BY-SA 3.0	added 672 characters in body
Aug 12, 2015 at 21:42	history	edited	Tomasz Kania	CC BY-SA 3.0	added 285 characters in body
Aug 12, 2015 at 11:47	vote	accept	Husaí Vázquez
Aug 12, 2015 at 8:44	comment	added	Tomasz Kania		If $X$ and $Y$ are infinite-dimensional Banach spaces and $\alpha$ is any reasonable crossnorm, then $X\odot_\alpha Y$ is incomplete. Choose two sequences of norm-one, linearly independent vectors $(x_n)$ and $(y_n)$ in $X$ and $Y$, respectively. Show that $(\sum_{k=1}^n \tfrac{1}{k^2}x_k\otimes y_k)$ is a Cauchy sequence without a limit in $X\odot_\alpha Y$.
Aug 12, 2015 at 4:24	comment	added	Husaí Vázquez		Do you know a reference to check that $L_1(\mu)\odot_{\varepsilon}X$ is complete if and only if $X$ is finite-dimensional. Anyways, thanks a lot for your help. I had been thinking for a while if those two spaces were complete.
Aug 11, 2015 at 21:30	history	edited	Tomasz Kania	CC BY-SA 3.0	added 149 characters in body
Aug 11, 2015 at 21:17	history	edited	Tomasz Kania	CC BY-SA 3.0	added 4 characters in body
Aug 11, 2015 at 21:10	history	answered	Tomasz Kania	CC BY-SA 3.0