论文标题
推导和对称操作员的扩展
Extensions of derivations and symmetric operators
论文作者
论文摘要
鉴于在真实或复杂的希尔伯特太空v上的密集定义的偏斜 - 对称操作员A 0，我们用收缩来参数所有M脉冲扩展，$φ$：H- $ \ rightarrow $ h +，其中手H +是Hilbert Spaces与边界四倍相关的Hilbert Space。当$φ$是统一操作员时，这种扩展就会产生统一C 0组。作为推论，我们获得了来自HTO H +的单位运算符的对称操作员的所有自相关扩展的参数化。我们的结果扩展了冯·诺伊曼（Von Neumann）发起的边界三元组理论，并由V. I.和M. L. Gorbachuk，J。Behrndt和M. Langer，S。A。Wegner和许多其他人开发，从某种意义上说，即使在对称情况下该缺陷指数不同）。
Given a densely defined skew-symmetric operators A 0 on a real or complex Hilbert space V , we parametrize all m-dissipative extensions in terms of contractions $Φ$ : H-$\rightarrow$ H + , where Hand H + are Hilbert spaces associated with a boundary quadruple. Such an extension generates a unitary C 0-group if and only if $Φ$ is a unitary operator. As corollary we obtain the parametrization of all selfadjoint extensions of a symmetric operator by unitary operators from Hto H +. Our results extend the theory of boundary triples initiated by von Neumann and developed by V. I. and M. L. Gorbachuk, J. Behrndt and M. Langer, S. A. Wegner and many others, in the sense that a boundary quadruple always exists (even if the defect indices are different in the symmetric case).
