A Characterization of Partial Isometries and Positive Operators in Hilbert Space
Keywords:
Polar Decomposition, Partial Isometries and Positive OperatorsAbstract
In this paper, we prove that if T is a bounded linear transformation U from one Hilbert space H to a Hilbert space K, then there exists a partial isometry U from H to K and a positive operator P such that T=UP.
Consequently, if T=UP is the polar decomposition of T, we find a necessary and sufficient condition that a partial isometry U is an isometry.
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2026-08-31
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Articles published in the Journal of Advanced Multidisciplinary Studies (JAMS) are licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), unless otherwise stated. Authors retain copyright of their work and grant JAMS the right of first publication.
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A Characterization of Partial Isometries and Positive Operators in Hilbert Space. (2026). Journal of Advanced Multidisciplinary Studies (JAMS), ABSTRACT No 02. https://jamsjournal.org/JAMS/article/view/characterization-partial-isometries-positive-operators-justus-mi
