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 -