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Let T = (T1, · · · ,Td) 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. Mathematics subject classification (2010): 47A05, 47A10, 47A11.

(A,m)-Symmetric commuting tuples of operators on a Hilbert space