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Abstract <p> The polar decomposition provides valuable insight into the nature of single-valued operators by expressing them as the product of a partial isometry and a nonnegative operator. Using a result by T. Kato, this article aims to present a general polar decomposition theorem for arbitrary closed linear relations, extending the classical theorem of polar decomposition of single-valued operators to the realm of closed multivalued operators, and to pave the way for its applications. </p>

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The Polar Decomposition Theorem for Closed Multivalued Operators

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. A. Aouichaoui

摘要

Abstract

The polar decomposition provides valuable insight into the nature of single-valued operators by expressing them as the product of a partial isometry and a nonnegative operator. Using a result by T. Kato, this article aims to present a general polar decomposition theorem for arbitrary closed linear relations, extending the classical theorem of polar decomposition of single-valued operators to the realm of closed multivalued operators, and to pave the way for its applications.