2024-03-28T22:41:45Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691582022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Generalized Numerical Radius And Unitary p-DilationNakazi, T.Okubo, K.numerical radiusnormp-dilation410In this paper, we,study an operator A on a Hilbert space H which satisfies one of the following inequalities For some ,\ with O ::; ,\ ::; 1 l(Ay, y)I ::; AIIYll2 + (1 - ,\)IIAYll2 (y EH) or AIIAYll2 + (1 - ,\)l(Ay, y)I ::; IIYll2 (y EH). These two inequalities can be regarded as special cases of generalized numerical ranges. If A has a p-dilation with p > 0, then it satisfies one of them. We show that the operator radii wp(A) of A are calculated using l(Ay,y)I and IIAYII- Several applications are given.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69158info:doi/10.14943/83554https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69158/1/pre408.pdfHokkaido University Preprint Series in Mathematics4081121998-04-01engpublisher