On representations and topological aspects of positive maps on non-unital quasi *-algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914942696816640 |
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| author | Ivkovic, Stefan Djordjevic, Bogdan D. Bellomonte, Giorgia |
| author_facet | Ivkovic, Stefan Djordjevic, Bogdan D. Bellomonte, Giorgia |
| contents | In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals, and noncommutative L2 spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2 space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On representations and topological aspects of positive maps on non-unital quasi *-algebras Ivkovic, Stefan Djordjevic, Bogdan D. Bellomonte, Giorgia Operator Algebras In this paper, we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals, and noncommutative L2 spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative L2 space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space. |
| title | On representations and topological aspects of positive maps on non-unital quasi *-algebras |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2405.09387 |