bio  website  math.tamu.edu/~johnson 

location  Texas A&M  
age  
visits  member for  4 years, 9 months 
seen  4 hours ago  
stats  profile views  9,116 
Distinguished Professor of Mathematics at Texas A&M University
1d

comment 
If any open set is a countable union of balls, does it imply separability?
Nice conclusion. 
Sep 14 
awarded  Nice Answer 
Sep 9 
comment 
$L^p$ norm means
Two papers that might be relevant are: G. Schechtman and J. Zinn, On the volume of the intersection of two $L^n_p$ balls, Proc. A.M.S. 110 (1990), 217–224. G. Schechtman and M. Schmuckenschlager, Another remark on the volume of the intersection of two $L^n_p$ balls, GAFA Seminar 89/90, Lecture Notes in Math., Vol 1469, 174–178, Springer (1991). 
Sep 3 
awarded  Necromancer 
Sep 3 
revised 
Surjectivity of operators on $\ell^\infty$
Fixed spelling in title. 
Sep 2 
comment 
Lipschitz function with somewhere dense image
What if you look at the image of a small ball around a point at which $f$ is differentiable? 
Sep 2 
revised 
Surjectivity of operators on $\ell^\infty$
added 165 characters in body 
Sep 2 
answered  Surjectivity of operators on $\ell^\infty$ 
Aug 29 
comment 
Proof of the DunfordPettis theorem
The book of Albiac and Kalton. 
Aug 28 
comment 
A formally weaker form of the extendable local reflexivity for Banach spaces
Each answer has a checkmark, visible only to the OP, below it. Click the checkmark to accept the answer. 
Aug 27 
comment 
“Direct” proof (without hypercontractivity) of equivalence of moments?
The most classical proof of Khintchine's inequality is obtained by proving it first for $p$ an even integer (just expand and compute). This gets the inequality for $p>2$. Then extrapolate to obtain it for $p<2$. This elementary proof gives the best order of constant, $\sqrt{p}$ as $p\to \infty$. The best constants were proved by Szarek ($p=2$) and Haagerup (general $p$) in the 1970s. 
Aug 22 
answered  Approaching convex and discrete geometry from other disciplines 
Aug 21 
comment 
Finitely generated groups nonembeddable into $L_1(0,1)$
What other classes of f.g. groups do Lipschitz embed into $L_1$? 
Aug 19 
comment 
A formally weaker form of the extendable local reflexivity for Banach spaces
You should accept my answer to keep this thread from coming to the front. 
Aug 15 
revised 
Two questions about convex subsets of Hilbert Space
edited tags 
Aug 15 
comment 
Two questions about convex subsets of Hilbert Space
If you replace $H$ by an arbitrary non reflexive space $X$, then the answer is "yes". James' theorem gives a norm one functional $F$ on $X$ which does not achieve its norm on the unit ball $B_X$ of $X$. Let $A = \{x\in X: 1 \le F(x)\} \cap 2B_X$ and set $B= B_X$. 
Aug 13 
comment 
Is the ideal of functions vanishing at a set complementable in $C(X)$?
The result Taka mentioned is due to K. Borsuk, Bull. Internat. Acad. Polon. Sci. Sér. A No. 113 (1933), 1–10. 
Aug 12 
answered  Is the ideal of functions vanishing at a set complementable in $C(X)$? 
Aug 10 
awarded  Nice Answer 
Aug 6 
answered  Norm of the upper triangular part of symmetric matrix 