Slant antieigenvalues and slant antieigenvectors of operators

We will introduce a general notion of slant antieigenvalue and corresponding slant antieigenvector. Then we establish how that theory may be compared to, and in some sense reduced to, the standard antieigenvalue theory. Generally speaking, our point of view is to accommodate such generalized antieigenvalue theories within the basic concepts and techniques of the original antieigenvalue theory.