Polar Decomposition for Non-Adjointable Maps

2025/12/06 by Skeide, Michael
#46L08 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2512.06335

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.

Citations

• Partial Isometries Between Hilbert Modules and Their Compositions

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