|
|
| |
| Tensor Products of Jacobson Radicals in Nest Algebras |
| |
Citation： |
DONG Zhe.Tensor Products of Jacobson Radicals in Nest Algebras[J].Chinese Annals of Mathematics B,2003,24(3):323~330 |
| Page view： 1228
Net amount： 849 |
Authors： |
DONG Zhe; |
|
|
| Abstract： |
This paper studies the tensor product $\rn\wo\mr$
of Jacobson radicals in nest algebras, and obtains that
$\rn\wo\mr=\{T\in\b(\h_{1}\otimes\h_{2}): T(N\otimes M)\sub
N_{-}\otimes M_{-},\forall N\in\n, M\in\m\}$; and based on the
characterization of rank-one operators in $\rn\wo\mr$, it is proved that
if $\n, \m$ are non-trivial then $\rn\wo\mr=\r_{\n\otimes\m}^{w}$ if
and only if $\n, \m$ are continuous. |
Keywords： |
Jacobson radical, Tensor product, Nest algebra |
Classification： |
47L75 |
|
|
Download PDF Full-Text
|
|
|
|
