G, Ramesh and P, Santhosh Kumar
(2016)
On the polar decomposition of right linear operators in quaternionic Hilbert spaces.
Journal of Mathematical Physics, 57 (4).
043502.
ISSN 00222488
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Abstract
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 U0 such that T=U0T. In fact U0 is unique if N(U0) = N(T). In particular, if H is separable and U is a partial isometry with T=UT, then we prove that U = U0 if and only if either N(T) = {0} or R(T)⊥ = {0}.
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