Slant joint antieigenvalues and antieigenvectors of operators in normal subalgebras

We will study the slant joint antieigenvalues and antieigenvectors of pairs of operators that belong to the same closed normal subalgebra of the algebra of bounded operators on a separable Hilbert space. This extends the slant antieigenvalue theory from single normal operators to pairs of normal operators. Our results may be viewed as extensions of the Greub-Rheinboldt inequality from two positive operators to two normal operators.