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

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 0022-2488

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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=U0|T|. In fact U0 is unique if N(U0) = N(T). In particular, if H is separable and U is a partial isometry with T=U|T|, then we prove that U = U0 if and only if either N(T) = {0} or R(T)⊥ = {0}.

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IITH Creators:	IITH Creators ORCiD G, Ramesh UNSPECIFIED
Item Type:	Article
Subjects:	Mathematics
Divisions:	Department of Mathematics
Depositing User:	Team Library
Date Deposited:	28 May 2019 10:59
Last Modified:	28 May 2019 10:59
URI:	http://raiithold.iith.ac.in/id/eprint/5358
Publisher URL:	http://doi.org/10.1063/1.4945314
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