Abstract
One of the couple of translatable radii of an operator in the direction of another operator introduced in earlier work [PAUL, K.: Translatable radii of an operator in the direction of another operator, Scientae Mathematicae 2 (1999), 119–122] 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 = λAf is obtained. Finally a theorem of Williams ([WILLIAMS, J. P.: Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129–136]) is generalized to obtain a translatable radius of an operator in the direction of another operator.
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Communicated by Michal Zajac
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Paul, K. Translatable radii of an operator in the direction of another operator II. Math. Slovaca 60, 121–128 (2010). https://doi.org/10.2478/s12175-009-0171-y
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DOI: https://doi.org/10.2478/s12175-009-0171-y