Polar Decomposition for Non-Adjointable Maps

Michael Skeide

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arXiv · 2512.06335

Polar Decomposition for Non-Adjointable Maps

Michael Skeide

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Abstract

We give conditions when not necessarily adjointable operators between Hilbert modules allow for a polar decomposition involving not necessarily adjointable partial isometries. While the latter have been introduced and discussed by Shalit and Skeide [SS23,Ske25], here we are led, as a basic new ingredient, to the notion of not necessarily adjointable operators $a$ that admit a modulus $|a|$, so-called modular operators.

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Michael Skeide. 2025-12-06. Polar Decomposition for Non-Adjointable Maps. https://arxiv.org/abs/2512.06335

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