Mixed multiplicativity and \(\ell _ p\) norms for matrices (Q1073136)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Mixed multiplicativity and \(\ell _ p\) norms for matrices |
scientific article; zbMATH DE number 3944045
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Mixed multiplicativity and \(\ell _ p\) norms for matrices |
scientific article; zbMATH DE number 3944045 |
Statements
Mixed multiplicativity and \(\ell _ p\) norms for matrices (English)
0 references
1986
0 references
The least constant \(\mu\) is discussed which satisfies \(N_ 1(AB)\leq \mu N_ 2(A)N_ 3(B)\) for given matrix norms \(N_ 1\), \(N_ 2\) and \(N_ 3\). \(\mu\) is explicitly determined if \(N_ 1\) \((N_ 2,N_ 3)\) is the \(\ell_ p\) \((\ell_ q,\ell_ r)\) norm \((1\leq p,q,r<\infty)\). The paper continues the work of the author and \textit{E. G. Straus} [ibid. 52-53, 351-360 (1983; Zbl 0516.15025) and 62, 1-10 (1984; Zbl 0547.15013)] where A, B and C are square matrices.
0 references
multiplicativity factor
0 references
submultiplicativity
0 references
matrix norms
0 references
0.94525003
0 references
0.91961795
0 references
0.90093017
0 references
0.89931977
0 references
0.89337724
0 references
