A very proper Heisenberg-Lie Banach *-algebra

作者：Laustsen Niels Jakob^*

来源：Positivity, 2012, 16(1): 67-79.

DOI：10.1007/s11117-011-0111-2

• Heisenberg-Lie commutation relations
• Banach *-algebra
• Very proper

For each pair of non-zero real numbers q(1) and q(2) Laustsen and Silvestrov have constructed a unital Banach *-algebra lq(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 is an element of N and a(1), ..., a(M) are elements of l(-1,1) such that Sigma(M)(m=1) a(m)* a(m) = 0, then necessarily a(1) = a(2) = ... = a(M) = 0.

• 出版日期2012-3