Year: 2007
Type: preprint
Abstract: We conjecture the following so-called norm compression inequality for $2\times N$ partitioned block matrices and the Schatten $p$-norms: for $p\ge 2$, $$ ||({array}{cccc} A_1 & A_2 & ... & A_N B_1 & B_2 & >... & B_N {array})||_p \le ||({array}{cccc} ||A_1||_p & ||A_2||_p & ... & ||A_N||_p \ ||B_1||_p & ||B_2||_p & ... & ||B_N||_p {array})||_p $$ while for $1\le p\le 2$ the ordering of the inequality is reversed. This inequality includes Hanner's inequality for matrices as a special case. We prove several special cases of this inequality and give examples for $3\times 3$ and larger partitionings where it does not hold.
Source: arXiv (Cornell University)
Author: Audenaert, Koenraad M. R.
Institution: London Institute for Mathematical Sciences
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7295279419
OpenAlex ID: W2952966136