2022-05-27T03:32:58Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692242018-04-25T23:44:07Zhdl_2115_45007hdl_2115_116Norm inequalities for some singular integral operatorsNakazi, T.Singular integral operatornormanalytic operator algebralifting theorem410Let B be a von Neumann algebra and Pa selfdjoint projection. For A and B in B, set S A,B = AP + BQ where Q = I - P. The operator S A,B will be called a singular integral operator. When B = L00(T) where LQ(.'(T) is the usual Lebesgue space on the unit circle and Pis an analytic projection, in [6] we established formulae for norms of SA,B and (SA,B)-1• In this paper, if A= {D E B : PDP = D} and (B, A, P) has a lifting property, then we will establish formulae of norms of S A,B and ( S A,B )-1. These formulae are operator theoretic and different from the previous ones. There are several examples such that (B, A, P) has a lifting property. As result, we give several interesting inequalities.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69224info:doi/10.14943/83620https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69224/1/pre474.pdfHokkaido University Preprint Series in Mathematics4741131999-11-01engpublisher