Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A very proper Heisenberg-Lie Banach *-algebra.
AU - Laustsen, Niels Jakob
N1 - 2010 Mathematics Subject Classification: primary 46K10; secondary 43A20.
PY - 2012/3
Y1 - 2012/3
N2 - 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.
AB - 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.
KW - Heisenberg-Lie commutation relations
KW - Banach -algebra
KW - very proper
U2 - 10.1007/s11117-011-0111-2
DO - 10.1007/s11117-011-0111-2
M3 - Journal article
VL - 16
SP - 67
EP - 79
JO - Positivity
JF - Positivity
SN - 1385-1292
IS - 1
ER -