bio  website  math.tamu.edu/~johnson 

location  Texas A&M  
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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.imjprg.fr/~gilles.pisier/ihppisier.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 estimateshe is using colloquial Banach space local theoryspeak. 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 $B=L_4$? 