(A, m)-SYMMETRIC COMMUTING TUPLES OF OPERATORS ON A HILBERT SPACE

Let T = (T-1,...,T-d) and A be a commuting d-tuple of operators and a positive operator on a complex Hilbert space, respectively. We introduce an (A, m) -symmetric commuting tuple of operators and characterize the joint approximate point spectrum of (A, m) -symmetric commuting tuple T. Next we introduce an (A, m) -expansive symmetric commuting tuple of operators and show basic properties of (A, m) -expansive symmetric commuting tuple.