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Distinguished Professor of Mathematics at Texas A&M University


20h
awarded  Nice Answer
Jun
18
comment Almost isometric embeddability implies isometric embeddability
I was thinking about the $\ell_p$ sum of a single space.
Jun
17
comment Almost isometric embeddability implies isometric embeddability
Proving that the condition is stable for infinite $\ell_p$ sums seems looks difficult. The ultra power of the $\ell_p$ sum of two spaces is the $\ell_p$ sum of the ultra power of the respective spaces, but there is not a version of that for infinite $\ell_p$ sums.
Jun
16
comment Almost isometric embeddability implies isometric embeddability
Any space that contains isometric copies of $\ell_\infty^n$ for all $n$ has the property.
Jun
16
answered Almost isometric embeddability implies isometric embeddability
Jun
15
comment Quadratic Variation of a Martingale in Hlibert Spaces
You might take a look at Pisier's course notes on martingales in Banach spaces: webusers.imj-prg.fr/~gilles.pisier/ihp-pisier.pdf
Jun
13
comment Subspaces and quotients in Banach space theory
For Q2: Let $X$ be reflexive. If $X$ embeds into $Y^*$, then $X^*$ is a quotient of $Y$. If $X$ is a quotient of $Y^*$, then $X^*$ need not embed into $Y$. $$$$ Another example: A quotient of a WCG space is WCG, but a subspace of a WCG space need not be WCG. (WCG = weakly compactly generated.)
Jun
12
awarded  Enlightened
Jun
6
comment Dose any infinite dimensional subspace contain the range of some one to one bounded linear operator?
Operator ranges are well studied. Googling "operator ranges" yields many relevant hits.
Jun
5
comment Dose any infinite dimensional subspace contain the range of some one to one bounded linear operator?
Same as yours, fedja.
Jun
3
comment An inequality for two independent identically distributed random vectors in a normed space
Thanks, fedja; with a few more points and $3.95 I can get an espresso. More seriously, you homed in on the essential points and I just added some windrow dressing. What attracted me (other than it being proposed by Pinelis) was that the answer violates Kwapien's dictum that probabilistic inequalities that are true for the real line are also true for Banach space random variables.
Jun
3
comment Zinn's “doubling” conjecture on weighted sums of independent Rademacher random variables
The link to T^2 does not work because it goes through your library.
Jun
3
comment An inequality for two independent identically distributed random vectors in a normed space
I added the missing minus sign.
Jun
3
revised An inequality for two independent identically distributed random vectors in a normed space
added 1 character in body
Jun
3
comment An inequality for two independent identically distributed random vectors in a normed space
Oh, there should be a minus sign in front of the fourth sample. Sorry for the typo.
Jun
2
revised An inequality for two independent identically distributed random vectors in a normed space
added 613 characters in body
Jun
2
answered An inequality for two independent identically distributed random vectors in a normed space
Jun
2
comment An inequality for two independent identically distributed random vectors in a normed space
Oops! You are right, Iosif; my arithmetic was bad, not for the first time. :)
Jun
2
comment A Banach space with all Hilbertian subspaces complemeneted
Yes, but it is clear from context that the proposer meant with estimates--he is using colloquial Banach space local theory-speak. One of us should have pointed that out in the above thread.
Jun
2
comment An inequality for two independent identically distributed random vectors in a normed space
OK, it is true if $B$ is $2$-dimensional or $L_p$, $1\le p\le 2$, because it is true when $B$ is the real line. But do you know whether it is true for $B=L_4$?