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Restricting operators to thick Hilbert C*-submodules
- Publication Year :
- 2024
-
Abstract
- Given an essential ideal $J\subset A$ of a C*-algebra $A$, and a Hilbert C*-module $M$ over $A$, we place $M$ between two other Hilbert C*-modules over $A$, $M_J\subset M\subset M^J$, 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 $M^J$.<br />Comment: 5 pages
- Subjects :
- Mathematics - Operator Algebras
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2404.04185
- Document Type :
- Working Paper