Self-adjoint algebras of unbounded operators
Self-adjoint algebras of unbounded operators
复制标题
无界算子的自伴代数
DOI：
10.1007/bf01646746
复制
发表时间：
1971
影响因子：
2.4
通讯作者：
R. Powers
中科院分区：
文献类型：
--
作者：
R. Powers
研究了*-代数的无界*-表示。被称为自伴表示的表示的定义类似于自伴算子的定义。结果表明，对于自伴表示，避免了某些与交换子空间和约化子空间相关的病理现象。为交换*-代数定义了一类行为良好的自伴表示，称为标准表示。证明了交换*-代数的强循环自伴表示是标准的当且仅当它是强正的，即它保持一定的序关系。对于有限个自由度的正则对易关系的*-表示也得到了类似的结果。
Unbounded *-representations of *-algebras are studied. Representations called self-adjoint representations are defined in analogy to the definition of a self-adjoint operator. It is shown that for self-adjoint representations certain pathologies associated with commutant and reducing subspaces are avoided. A class of well behaved self-adjoint representations, called standard representations, are defined for commutative *-algebras. It is shown that a strongly cyclic self-adjoint representation of a commutative *-algebra is standard if and only if the representation is strongly positive, i.e., the representations preserves a certain order relation. Similar results are obtained for *-representations of the canonical commutation relations for a finite number of degrees of freedom.