| Title:
|
Theorems of the alternative for cones and Lyapunov regularity of matrices (English) |
| Author:
|
Cain, Bryan |
| Author:
|
Hershkowitz, Daniel |
| Author:
|
Schneider, Hans |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
487-499 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Standard facts about separating linear functionals will be used to determine how two cones $C$ and $D$ and their duals $C^*$ and $D^*$ may overlap. When $T\:V\rightarrow W$ is linear and $K \subset V$ and $D\subset W$ are cones, these results will be applied to $C=T(K)$ and $D$, giving a unified treatment of several theorems of the alternate which explain when $C$ contains an interior point of $D$. The case when $V=W$ is the space $H$ of $n\times n$ Hermitian matrices, $D$ is the $n\times n$ positive semidefinite matrices, and $T(X) = AX + X^*A$ yields new and known results about the existence of block diagonal $X$’s satisfying the Lyapunov condition: $T(X)$ is an interior point of $D$. For the same $V$, $W$ and $D$, $ T(X)=X-B^*XB$ will be studied for certain cones $K$ of entry-wise nonnegative $X$’s. (English) |
| MSC:
|
15A24 |
| MSC:
|
15A48 |
| MSC:
|
15A57 |
| MSC:
|
46A40 |
| MSC:
|
46N10 |
| MSC:
|
52A05 |
| MSC:
|
90C48 |
| idZBL:
|
Zbl 0902.15011 |
| idMR:
|
MR1461427 |
| . |
| Date available:
|
2009-09-24T10:07:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127372 |
| . |
| Reference:
|
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| . |
