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Norm inequalities for some singular integral operators

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83620

Title: Norm inequalities for some singular integral operators
Authors: Nakazi, T. Browse this author
Keywords: Singular integral operator
norm
analytic operator algebra
lifting theorem
Issue Date: 1-Nov-1999
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 474
Start Page: 1
End Page: 13
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69224
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

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