TY - JOUR
T1 - A Quantum Harmonic Analysis Approach to Segal Algebras
AU - Berge, Eirik
AU - Berge, Stine Marie
AU - Fulsche, Robert
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/9
Y1 - 2024/9
N2 - 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.
AB - 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.
KW - 43A20
KW - 81S99
KW - Feichtinger algebra
KW - Primary 47B93
KW - Quantum harmonic analysis
KW - Secondary 47B48
KW - Segal algebra
UR - http://www.scopus.com/inward/record.url?scp=85196652788&partnerID=8YFLogxK
U2 - 10.1007/s00020-024-02771-w
DO - 10.1007/s00020-024-02771-w
M3 - Article
AN - SCOPUS:85196652788
VL - 96
JO - Integral Equations and Operator Theory
JF - Integral Equations and Operator Theory
SN - 0378-620X
IS - 3
M1 - 20
ER -