17,214 reputation
24184
bio website math.tamu.edu/~johnson
location Texas A&M
age
visits member for 4 years, 8 months
seen 9 hours ago

Distinguished Professor of Mathematics at Texas A&M University


16h
comment Finitely generated groups non-embeddable into $L_1(0,1)$
What other classes of f.g. groups do Lipschitz embed into $L_1$?
2d
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
Aug
5
comment Decreasing sequence of closed convex sets in a Banach space
Another obvious condition to get $C$ non empty is to assume that $E$ is reflexive and that the $C_n$ are bounded, closed and convex; or, more generally, that $E$ is a dual space and that the $C_n$ are bounded, weak$^*$ closed and convex.
Aug
5
comment The Banach space of bounded functions with countable support
Good questions. I have no idea how to attack them.
Aug
5
comment non-Borel set which intersects every compact in a Borel set
If $Y$ is the reals, your $X$ is neither locally compact nor metrizable.
Jul
27
comment Large subspaces with small basic constants in finite-dimensional Banach spaces
Have you checked what you can get from the technique in Mankiewicz, Piotr; Tomczak-Jaegermann, Nicole Embedding subspaces of ln∞ into spaces with Schauder basis. Proc. Amer. Math. Soc. 117 (1993), no. 2, 459–465? From the statement you just get that $f_B(n)$ is not linear, but I vaguely recall that they or somebody checked that $n^a$ was an upper bound for some specific $a<1$.
Jul
22
comment A formally weaker form of the extendable local reflexivity for Banach spaces
You are right. I was trying to do it so that you can get estimates depending on the dimension of $E$. Forget that and just enlarge $F$ and $E$ so that each is total over the other and choose $u_k$ Auerbach for $E$ and the unique biorthogonal $x_k^*$ in $F$, which must span $F$. Now you have no good estimate on the norms of the $x_k^*$. That does not matter because $\epsilon $ can be chosen small enough to compensate.
Jul
20
comment A formally weaker form of the extendable local reflexivity for Banach spaces
I gave an incorrect formula for $S$ and so have made an edit to my answer.
Jul
20
comment A formally weaker form of the extendable local reflexivity for Banach spaces
The norm condition on $x_k^*$ follows from the fact that $F$ almost norms $E$, which means that the natural mapping from $F$ to $E^*$ is almost (i.e., up to $1+\epsilon$) a quotient map.
Jul
20
revised A formally weaker form of the extendable local reflexivity for Banach spaces
added 829 characters in body
Jul
20
comment The reflexivity of the space generated by a convex, balanced and compact set
When people take the trouble to respond to a question on MO, the OP should be respond in timely fashion. You are being discourteous by not responding.
Jul
18
answered A formally weaker form of the extendable local reflexivity for Banach spaces
Jul
16
revised The reflexivity of the space generated by a convex, balanced and compact set
Corrected typo
Jul
16
comment The reflexivity of the space generated by a convex, balanced and compact set
I corrected a typo, Johannes; "and" should have been "on". By "weak topology from $X$" I mean the weak topology from $X^*$ which of course does not depend on $K$.