Reputation
Top tag
fa.functionalanalysis
7h

answered  Thin large subspaces of $\ell^N_1$ 
Nov
24 
comment 
On the operators from $l_{p}$ into Tsirelson's space $T$
No, Dongyang. Every operator from $\ell_p$ into $T$ is compact for every $1<p$. 
Nov
23 
revised 
When is the closed unit ball in a smaller Banach space closed in a larger Banach space?
Deleted Edit because it is not relevant after François' edit of the answer. 
Nov
23 
revised 
When is the closed unit ball in a smaller Banach space closed in a larger Banach space?
added 267 characters in body 
Nov
22 
answered  When is the closed unit ball in a smaller Banach space closed in a larger Banach space? 
Nov
22 
comment 
On the operators from $l_{p}$ into Tsirelson's space $T$
Yes. Same argument that works into $\ell_1$. 
Nov
21 
comment 
Equivalent definitions of $\mathscr{L}_p$spaces
It is really, really impolite to ask a question, get an answer, and vanish. 
Nov
17 
comment 
A characterization of relatively weakly $p$compact sets
I guess you mean weakly 1convergent rather than weakly 1summable. The answer is no; consider the summing basis for $c_0$. 
Nov
16 
comment 
A characterization of relatively weakly $p$compact sets
If $X$ is isomorphic to a quotient of $Y$, then $X^*$ is isomorphic to a subspace of $Y^*$. That is not the case herethe relevant $Y$ is super reflexive and the relevant $X$ is not. 
Nov
16 
comment 
A characterization of relatively weakly $p$compact sets
If $TB_Y \supset B_X$ then $T$ is surjective and $X$ is isomorphic to quotient of $Y$. What is there not to understand? 
Nov
16 
answered  A characterization of relatively weakly $p$compact sets 
Nov
15 
comment 
A characterization of relatively weakly $p$compact sets
You should add that $X$ is separable or replace "$B_{\ell_p^*}$" by "$B_{\ell_p^*(\Gamma)}$ for some $\Gamma$". 
Nov
12 
answered  On the normalized block basic sequences in $c_{0}\widehat{\otimes}_{\pi} c_{0}$ 
Nov
8 
comment 
What are some very important papers published in nontop journals?
One of the rare disagreements between Joram and me was over this. We wanted a paper in this volume dedicated to Kakutani and Joram said that we should publish the paper there. We knew that the lemma was neat and potentially useful since it eliminated the "curse of dimensionality" in certain high dimensional pattern recognition problems and I was worried that putting it in a proceedings volume would bury it. Joram said, "If the lemma is useful, people will find it." As usual, Joram was right, but he did take the trouble to tell Nati Linial about the lemma, and Nati named and publicized it. 
Nov
7 
comment 
What are some very important papers published in nontop journals?
Thanks for the info, Jerry. It would be a better story if you had submitted the paper to the Annals and had it rejected. :) 
Nov
6 
comment 
What are some very important papers published in nontop journals?
Even more interesting would be self references along with an explanation of why a paper appeared in a lesser journal. 
Nov
6 
answered  Equivalent definitions of $\mathscr{L}_p$spaces 
Oct
29 
comment 
Weakly $p$summable sequences in $L_{r}$
For a proof that does not mention cotype see $$$$ Rosenthal, Haskell P. On quasicomplemented subspaces of Banach spaces, with an appendix on compactness of operators from Lp(μ) to Lr(ν). J. Functional Analysis 4 1969 176–214. 
Oct
29 
answered  Weakly $p$summable sequences in $L_{r}$ 
Oct
26 
comment 
HahnBanach theorem with convex majorant
I don't understand, Christian. If you are dealing with normed spaces you need the separation theorem, which more or less forces you to prove the subllnear version. 