Publication Date:
2016-04-08
Description:
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 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 ) ⊥ = {0}.
Print ISSN:
0022-2488
Electronic ISSN:
1089-7658
Topics:
Mathematics
,
Physics
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