Bounded modular functionals and operators on Hilbert C*-modules that are regular
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911575709843456 |
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| author | Frank, Michael Ivanescu, Cristian |
| author_facet | Frank, Michael Ivanescu, Cristian |
| contents | We find first structural background information about the reasons that for any C*-algebra $A$ and any two Hilbert $A$-modules $M \subseteq N$ with $M^\perp=\{0\}$, every bounded $A$-linear map $N \to A$ (or $N \to N)$ vanishing on $M$ might be only the zero map. The self-adjoint case is proved, whereas the general case is open with partial insights.
Unfortunately, the proof of Lemma 3.3 of our first version contains the implicit assumption that the projection $P$ and the operator $S$ commute, which is not the case for non-zero non-self-adjoint operators $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24042 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bounded modular functionals and operators on Hilbert C*-modules that are regular Frank, Michael Ivanescu, Cristian Operator Algebras Functional Analysis 46L08 (Primary) 46L05, 47A20, 54D15 (Secondary) We find first structural background information about the reasons that for any C*-algebra $A$ and any two Hilbert $A$-modules $M \subseteq N$ with $M^\perp=\{0\}$, every bounded $A$-linear map $N \to A$ (or $N \to N)$ vanishing on $M$ might be only the zero map. The self-adjoint case is proved, whereas the general case is open with partial insights. Unfortunately, the proof of Lemma 3.3 of our first version contains the implicit assumption that the projection $P$ and the operator $S$ commute, which is not the case for non-zero non-self-adjoint operators $S$. |
| title | Bounded modular functionals and operators on Hilbert C*-modules that are regular |
| topic | Operator Algebras Functional Analysis 46L08 (Primary) 46L05, 47A20, 54D15 (Secondary) |
| url | https://arxiv.org/abs/2603.24042 |