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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


Mar
25
comment reflexive banach space
Thanks, Tim; I corrected.
Mar
25
revised reflexive banach space
Corrected typo spelling.
Mar
24
answered reflexive banach space
Mar
24
comment reflexive banach space
OK, I turned it into an answer now that the question has been reopened.
Mar
24
revised reflexive banach space
Added tag to bump this question because there is a good answer that I put in a comment.
Mar
24
comment reflexive banach space
A separable Banach space is reflexive iff there is an equivalent norm on the space s.t. whenever $(x_n)$ is a bounded sequence for which $\lim_n \lim_m \|x_n + x_m\| = 2 \lim_n \|x_n\|$, the sequence $(x_n)$ converges.
Mar
24
comment reflexive banach space
There is a beautiful result of Odell and Schlumprecht that gives an answer to this question for separable Banach spaces.Odell, E.(1-TX); Schlumprecht, Th.(1-TXAM) Asymptotic properties of Banach spaces under renormings. (English summary) J. Amer. Math. Soc. 11 (1998), no. 1, 175–188.
Mar
24
comment Uninteresting questions with interesting answers
Is this the easiest proof that $\pi < 22/7$? :)
Mar
22
comment A convex analysis theorem improvement
Sure, if the norm generated by the body has good properties such as type. For example, if the resulting space embeds into $L_p$ isometrically the upper estimate is $n^{|1/p - 1/2|}$ (result of D. R. Lewis).
Mar
22
answered A question in Banach space
Mar
21
comment A convex analysis theorem improvement
The cube witnesses that it is sharp. Look at Chapter 12 in the book by Albiac and Kalton, or, for more, consult Nicole Tomczak-Jaegermann's book.
Mar
19
comment How many subsets of $[0,1)$ are there modulo null sets?
Vote up this comment if you (as I) think that JDH should NOT delete his answer.
Mar
18
answered Infinite direct sum of $l_2^{(n_k)}$ contains a complemented isometric copy of $l_2$
Mar
18
comment Images of $\{0,1\}^\kappa$
It is worth noting that every compact Hausdorff space is the continuous image of a closed subset of some product of $\{0,1\}$. You can find this in standard books; in particularly, Kelley's "General Topology".
Mar
6
answered Ultraweak topology on B(X): Is the map X\otimes X* -> B(X)* isometric?
Mar
4
awarded  Enlightened
Mar
4
awarded  Nice Answer
Mar
1
revised Ultraweak topology on B(X): Is the map X\otimes X* -> B(X)* isometric?
Added missing phrase
Feb
28
revised Ultraweak topology on B(X): Is the map X\otimes X* -> B(X)* isometric?
Added reference
Feb
28
answered Ultraweak topology on B(X): Is the map X\otimes X* -> B(X)* isometric?