TY - JOUR

T1 - Logarithmic submajorization, uniform majorization and Hölder type inequalities for τ-measurable operators

AU - Dodds, P. G.

AU - Dodds, T. K.

AU - Sukochev, F. A.

AU - Zanin, D.

PY - 2020/9

Y1 - 2020/9

N2 - We extend the notion of the determinant function Λ, originally introduced by T.Fack for τ-compact operators, to a natural algebra of τ-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Hölder type inequalities via general Araki–Lieb–Thirring inequalities due to Kosaki and Han and to a Weyl-type theorem for uniform majorization.

AB - We extend the notion of the determinant function Λ, originally introduced by T.Fack for τ-compact operators, to a natural algebra of τ-measurable operators affiliated with a semifinite von Neumann algebra which coincides with that defined by Haagerup and Schultz in the finite case and on which the determinant function is shown to be submultiplicative. Application is given to Hölder type inequalities via general Araki–Lieb–Thirring inequalities due to Kosaki and Han and to a Weyl-type theorem for uniform majorization.

KW - Fuglede–Kadison theorem

KW - Logarithmic submajorization

KW - Measurable operators

KW - Semifinite von Neumann algebra

KW - Uniform majorization

UR - http://www.scopus.com/inward/record.url?scp=85080145224&partnerID=8YFLogxK

U2 - 10.1016/j.indag.2020.02.004

DO - 10.1016/j.indag.2020.02.004

M3 - Article

AN - SCOPUS:85080145224

VL - 31

SP - 809

EP - 830

JO - INDAGATIONES MATHEMATICAE-NEW SERIES

JF - INDAGATIONES MATHEMATICAE-NEW SERIES

SN - 0019-3577

IS - 5

ER -