@article{dc23237ceedf4b80b3cfacd95988d3b1, title = "A Quantum Harmonic Analysis Approach to Segal Algebras", abstract = "In this article, we study a commutative Banach algebra structure on the space L1(R2n)⊕T1, where the T1 denotes the trace class operators on L2(Rn). The product of this space is given by the convolutions in quantum harmonic analysis. Towards this goal, we study the closed ideals of this space, and in particular its Gelfand theory. We additionally develop the concept of quantum Segal algebras as an analogue of Segal algebras. We prove that many of the properties of Segal algebras have transfers to quantum Segal algebras. However, it should be noted that in contrast to Segal algebras, quantum Segal algebras are not ideals of the ambient space. We also give examples of different constructions that yield quantum Segal algebras.", keywords = "43A20, 81S99, Feichtinger algebra, Primary 47B93, Quantum harmonic analysis, Secondary 47B48, Segal algebra", author = "Eirik Berge and Berge, {Stine Marie} and Robert Fulsche", note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.", year = "2024", month = sep, doi = "10.1007/s00020-024-02771-w", language = "English", volume = "96", journal = "Integral Equations and Operator Theory", issn = "0378-620X", publisher = "Birkhauser Verlag Basel", number = "3", }