Geodesic
On submajorisation of the Rotfeld's inequality
Filomat, Tome 37 (2023) no. 21, p. 7009

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DOI

Let (M, τ) be a semi-finite von Neumann algebra, L0(M) be the set of all τ-measurable operators, µt(x) be the generalized singular number of x ∈ L0(M). We proved that if 1 : [0,∞) → [0,∞) is an increasing continuous function, then for any x, y in L0(M), µt(1(|x + y|)) ≤ µt(1( 12 ( |x| + |y| x∗ + y∗ x + y |x∗| + |y∗| ) )), 0 t τ(1). We also obtained that if f : [0,∞) → [0,∞) is a concave function, then µ( f ( 12 ( |x| + |y| x∗ + y∗ x + y |x∗| + |y∗| ) )) is submajorized by µ( f (|x|)) + µ( f (|y|)).
DOI : 10.2298/FIL2321009A
Classification : 46L52, 47L05
Keywords: Rotfeld’s inequality, τ-measurable operator, submajorisation, semifinite von Neumann algebra 
Maktagul Alday; Serik Kudaibergenov. On submajorisation of the Rotfeld's inequality. Filomat, Tome 37 (2023) no. 21, p. 7009 . doi: 10.2298/FIL2321009A
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     title = {On submajorisation of the {Rotfeld's} inequality},
     journal = {Filomat},
     pages = {7009 },
     year = {2023},
     volume = {37},
     number = {21},
     doi = {10.2298/FIL2321009A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2321009A/}
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