A very proper Heisenberg-Lie Banach *-algebra.

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

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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
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:	28 Aug 2012 09:34
Identification Number:
URI:	http://eprints.lancs.ac.uk/id/eprint/34845

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