, Volume 16, Issue 1, pp 67–79 | Cite as

A very proper Heisenberg–Lie Banach *-algebra



For each pair of non-zero real numbers q 1 and q 2, Laustsen and Silvestrov have constructed a unital Banach *-algebra \({\fancyscript{C}_{q_1,q_2}}\) which contains a universal normalized solution to the *-algebraic (q 1, q 2)-deformed Heisenberg–Lie commutation relations. We show that for (q 1, q 2) = (−1, 1), this Banach *-algebra is very proper; that is, if \({M\in\mathbb{N}}\) and \({a_1, \ldots, a_M}\) are elements of \({\fancyscript{C}_{-1,1}}\) such that \({\sum_{m=1}^M a_m^*a_m=0}\), then necessarily \({a_1=a_2=\cdots=a_M=0}\).


Heisenberg–Lie commutation relations Banach *-algebra Very proper 

Mathematics Subject Classification (2010)

Primary 46K10 Secondary 43A20 


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, Fylde CollegeLancaster UniversityLancasterUK

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