2023-09-29T10:13:10Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/692242022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Norm inequalities for some singular integral operatorsNorm inequalities for some singular integral operatorsNakazi, T.Nakazi, T.Singular integral operatornormanalytic operator algebralifting theoremSingular integral operatornormanalytic operator algebralifting theorem410410Let 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.Let 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.Department of Mathematics, Hokkaido UniversityDepartment of Mathematics, Hokkaido UniversityDepartmental Bulletin PaperDepartmental Bulletin Paperapplication/pdfapplication/pdfhttp://hdl.handle.net/2115/69224http://hdl.handle.net/2115/69224info:doi/10.14943/83620info:doi/10.14943/83620https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69224/1/pre474.pdfhttps://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69224/1/pre474.pdfHokkaido University Preprint Series in MathematicsHokkaido University Preprint Series in Mathematics4744741113131999-11-011999-11-01engengpublisherpublisher