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

Abstract

In this article we prove the existence of the polar decomposition for 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 $T=U_0|T|$. 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 $T=U|T|$, then we prove that $U=U_0$ if and only if either $N(T)=\{0\}$ or $R(T{)}^{\perp }=\{0\}$.

17 pages

References in corpus (1)

• Continuous slice functional calculus in quaternionic Hilbert spaces

Cited by in corpus (2)

• A note on convexity of sections of quaternionic numerical range
• Strongly irreducible factorization of quaternionic operators and Riesz decomposition theorem