Abstract
The purpose of the paper is to introduce and study a class of multivariable operators on semi-Hilbertian spaces, i.e. spaces generated by positive semidefinite sesquilinear forms. Let
and let A be a commuting m-tuple of operators and a positive operator on a complex Hilbert space, respectively. We introduce an A-hyponormal tuple of operators and study some properties of this class of multivariable operators. An m-tuple of operators
is said to be A-hyponormal tuple if
for each finite collections