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bio website math.tamu.edu/~johnson
location Texas A&M
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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 Dunford-Pettis 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 non-embeddable 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