On the polar decomposition of right linear operators in quaternionic Hilbert spaces

摘要

In this article, we prove the existence of the polar decomposition of densely defined closed right linear operators in quaternionic Hilbert spaces: If T is a 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 vertical bar T vertical bar. In fact U-0 is unique if N(U-0) = N(T). In particular, if H is separable and U is a partial isometry with T = U vertical bar T vertical bar, then we prove that U = U-0 if and only if either N(T) = {0} or R(T)(perpendicular to) = {0}. (C) 2016 AIP Publishing LLC.