In this article we prove the existence of the polar decomposition for denselydefined closed right linear operators in quaternionic Hilbert spaces: If $T$ isa densely defined closed right linear operator in a quaternionic Hilbert space$H$, then there exists a partial isometry $U_{0}$ such that $T = U_{0}|T|$. Infact $U_{0}$ is unique if $N(U_{0}) = N(T)$. In particular, if $H$ is separableand $U$ is a partial isometry with $T = U|T|$, then we prove that $U = U_{0}$if and only if either $N(T) = \{0\}$ or $R(T)^{\bot} = \{0\}$.
展开▼
机译：在本文中，我们证明了四元离子希尔伯特空间中稠密定义的封闭右线性算子的极分解存在：如果$ T $是四元离子希尔伯特空间$ H $中的稠密定义的右线性算子，则存在部分等轴测度$ U_ {0} $，这样$ T = U_ {0} | T | $。如果$ N（U_ {0}）= N（T）$，则事实$ U_ {0} $是唯一的。特别是，如果$ H $是可分离的，并且$ U $是具有$ T = U | T | $的部分等轴测图，则我们证明$ U = U_ {0} $ if并且仅当$ N（T）= \ {0 \} $或$ R（T）^ {\ bot} = \ {0 \} $。
展开▼
