Translatable radii of an operator in the direction of another operator II

Abstract

One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work[13] is studied in details. A necessary and sufficient condition for a unit vector f to be a stationary vector of the generalized eigenvalue problem $ Tf = \lambda A f $ is obtained. Finally a theorem of Williams[16] is generalized to obtain a translatable radius of an operator in the direction of another operator.