On (n1, <middle dot> <middle dot><middle dot>, nm)-hyponormal tuples of Hilbert space operators

This paper introduces a new class of multivariable operators called (n(1), <middle dot> <middle dot> <middle dot>, n(m) )- hyponormal tuples, which combine joint normal and joint hyponormal operators. A tuple of operators Q = (Q(1),<middle dot><middle dot><middle dot>, <middle dot><middle dot><middle dot> , Q(m)) is said to be an (n(1), <middle dot> <middle dot> <middle dot>, n(m) )-hyponormal tuple for some (n(1), <middle dot> <middle dot> <middle dot>, n(m)) is an element of N-m if Sigma(1 <= k, l <= m) <[Qk(& lowast;)n(k ) , Q(l)(nl) ] omega(k) | omega(l) >= 0 , for all ( omega k ) (1 <= k <= m )is an element of K m . We show several properties of this class that correspond to the properties of joint hyponormal operators.