Linear Maps Preserving the Closure of Numerical Range on Nest Algebras with Maximal Atomic Nest
Linear Maps Preserving the Closure of Numerical Range on Nest Algebras with Maximal Atomic Nest
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DOI：
10.1007/s00020-001-1140-1
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发表时间：
2003-07
影响因子：
0.8
通讯作者：
Jianlian Cui;J. Hou
中科院分区：
文献类型：
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作者：
Jianlian Cui;J. Hou
令 为希尔伯特空间上的最大原子嵌套并表示相关联的嵌套代数。我们证明弱连续满射线性映射当且仅当存在酉算子使得对于每个或对于每个，其中表示 Trelative 到任意但固定的 H 基的转置。作为应用，我们得到了数值范围或数值半径保护器的特征。还描述了保持数值范围闭包或保持数值范围（半径）的原子巢代数的对角代数上的满射线性映射。
Letbe a maximal atomic nest on Hilbert spaceHanddenote the associated nest algebra. We prove that a weakly continuous andsurjective linear mappreserves the closure of numericalrange if and only if there exists a unitary operatorsuch thatfor everyorfor every,wheredenotes the transpose ofTrelative to an arbitrary but fixed baseofH. As applications, we get the characterizations of the numerical rangeor numerical radius preservers on. The surjective linear maps on the diagonal algebras of atomic nest algebras preserving the closure of numerical range or preserving the numerical range (radius) are also characterized.