Restricting operators to thick Hilbert C*-submodules

2024/04/05 by Vladimir Manuilov, Manuilov, V.
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Banach Space Theory #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2404.04185

openalex publication_date 2024/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given an essential ideal J⊂ A of a C*-algebra A, and a Hilbert C*-module M over A, we place M between two other Hilbert C*-modules over A, M_J⊂ M⊂ M^J, in such a way that each submodule here is thick, i.e. its orthogonal conmplement in the greater module is trivial. We introduce the class \mathbb B_J(M) of J-adjointable operators on a Hilbert C*-module M over A, and prove that this class isometrically embeds into the C*-algebras of all adjointable operators both of M_J and of M^J.

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