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Distinguished Professor of Mathematics at Texas A&M University


2d
comment Dual of pre-dual of BV
See Pełczyński, Aleksander; Wojciechowski, Michał Spaces of functions with bounded variation and Sobolev spaces without local unconditional structure. J. Reine Angew. Math. 558 (2003), 109–157. I cannot access the paper right now, but I think it contains the information you seek.
Dec
18
comment Uniformly bounded operator family and pointwise convergence
If $f_n \to f$ a.e. and $\|f_n\|_p \to \|f\|_p$ then $\|f-f_n\|_p \to 0$ for any $p<\infty$. This is problem 6.10 in Folland's Real Analysis and is in many other RA books. Clarkson is not needed for the proof.
Dec
15
answered Rademacher type of a Banach space is always less than or equal to 2
Dec
13
awarded  Yearling
Nov
30
awarded  Nice Answer
Nov
28
comment Reflexive subspaces of non-separable abstract $L_1$ spaces
Nice, Tomek. I missed that even after using Maharam's theorem recently.
Nov
28
comment Bounded operator on a normed space with empty spectrum
Your clarification of "spectrum" was essential, since every bounded operator on a normed space has an approximate eigenvalue.
Nov
27
comment Reflexive subspaces of non-separable abstract $L_1$ spaces
$\ell_p(I)$ is easy, because $L_1[0,1]^I$ obviously contains an IID family of size $|I|$ of $p$-stable random variables. If the classical approach for embedding $L_p[0,1]$ into $L_1[0,1]$ does not obviously generalize, try the approach that Maurey, Schechtman, and I used in our Memoirs.
Nov
19
comment Contractively complemented subspaces of $c_0(I)$
Why did not not correct the other three mistakes, Yemon? :)
Nov
4
revised James $\ell_1$-theorem
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Nov
4
answered James $\ell_1$-theorem
Nov
2
comment Existence of a mapping in a nonseparable Banach space
Why are you interested in having such a map?
Oct
29
comment Triangle inequality for $L^1$-norm with respect to a state
Have you read the Pisier-Xu article in the Handbook of the Geometry of Banach Spaces? It is online: $$ $$ dmitripavlov.org/scans/pisier-xu.pdf
Oct
29
comment CB-norm of mappings from a matrix space
Did you ask Gilles? He does not follow MO as far as I know.
Oct
26
comment Generalised “projection” of a metric space
We've all been there, J. Fabian. I hope you did not my "joke" answer, which was the most complicated proof I saw off the top of my head. I was hoping that someone would suggest eliminating the axiom of choice by quoting the non linear Hahn-Banach theorem instead of the Hahn-Banach theorem, but apparently no one else was in a jovial mood.
Oct
26
comment Generalised “projection” of a metric space
IMO, as a simple answer one should give $f(x) = d(x,p_0)$.
Oct
25
answered Generalised “projection” of a metric space
Oct
23
awarded  Enlightened
Oct
23
awarded  Nice Answer
Oct
21
revised A lower bound on $\|\cdot\|_{p_{\ast}}$ image of $\ell^{q_{\ast}}$ vectors
added 5 characters in body