Geodesic
Generalized induced norms
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 127-133 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $\Vert {\cdot }\Vert $ be a norm on the algebra ${\mathcal M}_n$ of all $n\times n$ matrices over ${\mathbb{C}}$. An interesting problem in matrix theory is that “Are there two norms $\Vert {\cdot }\Vert _1$ and $\Vert {\cdot }\Vert _2$ on ${\mathbb{C}}^n$ such that $\Vert A\Vert =\max \lbrace \Vert Ax\Vert _{2}\: \Vert x\Vert _{1}=1\rbrace $ for all $A\in {\mathcal M}_n$?” We will investigate this problem and its various aspects and will discuss some conditions under which $\Vert {\cdot }\Vert _1=\Vert {\cdot }\Vert _2$.
Let $\Vert {\cdot }\Vert $ be a norm on the algebra ${\mathcal M}_n$ of all $n\times n$ matrices over ${\mathbb{C}}$. An interesting problem in matrix theory is that “Are there two norms $\Vert {\cdot }\Vert _1$ and $\Vert {\cdot }\Vert _2$ on ${\mathbb{C}}^n$ such that $\Vert A\Vert =\max \lbrace \Vert Ax\Vert _{2}\: \Vert x\Vert _{1}=1\rbrace $ for all $A\in {\mathcal M}_n$?” We will investigate this problem and its various aspects and will discuss some conditions under which $\Vert {\cdot }\Vert _1=\Vert {\cdot }\Vert _2$.
Classification : 15A60, 46B99, 47A30
Keywords: induced norm; generalized induced norm; algebra norm; the full matrix algebra; unitarily invariant; generalized induced congruent 
@article{CMJ_2007_57_1_a10,
     author = {Hejazian, S. and Mirzavaziri, M. and Moslehian, M. S.},
     title = {Generalized induced norms},
     journal = {Czechoslovak Mathematical Journal},
     pages = {127--133},
     year = {2007},
     volume = {57},
     number = {1},
     mrnumber = {2309954},
     zbl = {1174.15016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a10/}
}
TY  - JOUR
AU  - Hejazian, S.
AU  - Mirzavaziri, M.
AU  - Moslehian, M. S.
TI  - Generalized induced norms
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 127
EP  - 133
VL  - 57
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a10/
LA  - en
ID  - CMJ_2007_57_1_a10
ER  - 
%0 Journal Article
%A Hejazian, S.
%A Mirzavaziri, M.
%A Moslehian, M. S.
%T Generalized induced norms
%J Czechoslovak Mathematical Journal
%D 2007
%P 127-133
%V 57
%N 1
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a10/
%G en
%F CMJ_2007_57_1_a10
Hejazian, S.; Mirzavaziri, M.; Moslehian, M. S. Generalized induced norms. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 1, pp. 127-133. http://geodesic.mathdoc.fr/item/CMJ_2007_57_1_a10/