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A very proper Heisenberg-Lie Banach *-algebra.

Research output: Contribution to journalJournal article


<mark>Journal publication date</mark>03/2012
Issue number1
Number of pages13
Pages (from-to)67-79
<mark>Original language</mark>English


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.

Bibliographic note

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