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Results tagged with banach-spaces
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user 8430
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
53
votes
Accepted
Absolute value inequality for complex numbers
It seems that your inequality is just an incarnation of Hlawka's inequality
which says that for any vectors $x, y, z$ in an inner product space $V$ we have
\begin{equation*}
\|x+y\| + \|y+z\|+\|z+x …
- 28.6k
3
votes
How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?
EDIT. In light of Nathaniel's answer above, I must admit that the hardness intuition was wrong, and the problem is indeed tractable. However, I'm leaving the original answer as is, to preserve the con …
- 28.6k
4
votes
$\|T\|_2 \le \sqrt{\|T\|_1\|T\|_\infty}$
Sorry, my answer below is only partial, but I thought that it may still be somewhat interesting.
As far as I know, this inequality does not have a distinguished name. It is ultimately a consequence …
- 28.6k
7
votes
Norms of commutators
In a recent paper ([1]), Ravichandran and Srivastava (RS) study pavings for collections of matrices. Their main theorem claims to yield an improvement to the bound obtained by Johnson, Ozawa, and Sche …
- 28.6k
8
votes
Norms of commutators
Almost the references cited below discuss upper bounds (i.e., norm(commutator) $\le$ something). One of the most relevant results is in reference #3 that I alluded to in my comment above.
A short not …
- 28.6k
11
votes
Accepted
What is the "positive part" of the unit ball in $M_n(R)$ ?
I'm a bit late in answering this. But in case there is still interest, please have a look at:
Saunderson, Parrilo, Willsky. Semidefinite descriptions of the convex hull of rotation matrices, SIAM J. …
- 28.6k