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arXiv · 2405.09387

On representations and topological aspects of positive maps on non-unital quasi *-algebras

Stefan Ivkovic·Bogdan D. Djordjevic·Giorgia Bellomonte
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Abstract

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.

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Stefan Ivkovic, Bogdan D. Djordjevic, Giorgia Bellomonte. 2024-05-15. On representations and topological aspects of positive maps on non-unital quasi *-algebras. https://doi.org/10.1007/s11117-024-01079-8

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