Laustsen, Niels Jakob (2012) *A very proper Heisenberg-Lie Banach *-algebra.* Positivity, 16 (1). pp. 67-79. ISSN 1385-1292

Official URL: http://dx.doi.org/10.1007/s11117-011-0111-2

## Abstract

For each pair of non-zero real numbers q_1 and q_2, Laustsen and Silvestrov have constructed a unital Banach *-algebra C_{q_1,q_2} which contains a universal normalized solution to the *-algebraic (q_1,q_2)-deformed Heisenberg-Lie commutation relations. We show that in the case where (q_1,q_2) = (1,-1) or (q_1,q_2) = (-1,1), this Banach *-algebra is very proper; that is, if M is a natural number and a_1,..., a_M are elements of either C_{1,-1} or C_{-1,1} such that a_1^*a_1 + a_2^*a_2 + ... + a_M^*a_M = 0, then necessarily a_1 = a_2 = ... = a_M = 0.

Item Type: | Article |
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Journal or Publication Title: | Positivity |

Additional Information: | 2010 Mathematics Subject Classification: primary 46K10; secondary 43A20. |

Uncontrolled Keywords: | Heisenberg-Lie commutation relations ; Banach *-algebra ; very proper |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 34845 |

Deposited By: | Dr Niels Jakob Laustsen |

Deposited On: | 13 Dec 2010 16:11 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 22 Oct 2016 01:44 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/34845 |

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