| Title:
|
Generalized induced norms (English) |
| Author:
|
Hejazian, S. |
| Author:
|
Mirzavaziri, M. |
| Author:
|
Moslehian, M. S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
57 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
127-133 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Vert {\cdot }\Vert _1=\Vert {\cdot }\Vert _2$. (English) |
| Keyword:
|
induced norm |
| Keyword:
|
generalized induced norm |
| Keyword:
|
algebra norm |
| Keyword:
|
the full matrix algebra |
| Keyword:
|
unitarily invariant |
| Keyword:
|
generalized induced congruent |
| MSC:
|
15A60 |
| MSC:
|
46B99 |
| MSC:
|
47A30 |
| idZBL:
|
Zbl 1174.15016 |
| idMR:
|
MR2309954 |
| . |
| Date available:
|
2009-09-24T11:44:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128160 |
| . |
| Reference:
|
[1] G. R. Belitskiĭ, Yu. I. Lyubich: Matrix Norms and Their Applications. Operator Theory: Advances and Applications, 36.Birkhäuser-Verlag, Basel, 1988. MR 1015711 |
| Reference:
|
[2] R. Bhatia: Matrix Analysis. Graduate Texts in Mathematics, 169.Springer-Verlag, New York, 1997. MR 1477662 |
| Reference:
|
[3] R. A. Horn, C. R. Johnson: Matrix Analysis.Cambridge University Press, Cambridge, 1994. MR 1084815 |
| Reference:
|
[4] C.-K. Li, N.-K. Tsing, and F. Zhang: Norm hull of vectors and matrices.Linear Algebra Appl. 257 (1997), 1–27. MR 1441701 |
| Reference:
|
[5] W. Rudin: Real and Complex Analysis.McGraw-Hill, New York, 1987. Zbl 0925.00005, MR 0924157 |
| . |
