symmetric operator spaces
Recently Published Documents


TOTAL DOCUMENTS

20
(FIVE YEARS 0)

H-INDEX

7
(FIVE YEARS 0)

2019 ◽  
Vol 169 (3) ◽  
pp. 607-622
Author(s):  
JINGHAO HUANG ◽  
GALINA LEVITINA ◽  
FEDOR SUKOCHEV

AbstractLet ℳ be a semifinite von Neumann algebra with a faithful semifinite normal trace τ. Assume that E(0, ∞) is an M-embedded fully symmetric function space having order continuous norm and is not a superset of the set of all bounded vanishing functions on (0, ∞). In this paper, we prove that the corresponding operator space E(ℳ, τ) is also M-embedded. It extends earlier results by Werner [48, Proposition 4∙1] from the particular case of symmetric ideals of bounded operators on a separable Hilbert space to the case of symmetric spaces (consisting of possibly unbounded operators) on an arbitrary semifinite von Neumann algebra. Several applications are given, e.g., the derivation problem for noncommutative Lorentz spaces ℒp,1(ℳ, τ), 1 < p < ∞, has a positive answer.





2015 ◽  
Vol 228 (1) ◽  
pp. 47-54 ◽  
Author(s):  
Ken Dykema ◽  
Anna Skripka


2014 ◽  
Vol 414 (2) ◽  
pp. 742-755 ◽  
Author(s):  
E.M. Semenov ◽  
F.A. Sukochev




2008 ◽  
Vol 51 (1) ◽  
pp. 67-80 ◽  
Author(s):  
Nigel Kalton ◽  
Fyodor Sukochev

AbstractWe present a construction of singular rearrangement invariant functionals on Marcinkiewicz function/operator spaces. The functionals constructed differ from all previous examples in the literature in that they fail to be symmetric. In other words, the functional ϕ fails the condition that if (Hardy-Littlewood-Polya submajorization) and 0 ≤ x, y, then 0 ≤ ϕ(x) ≤ ϕ(y). We apply our results to singular traces on symmetric operator spaces (in particular on symmetrically-normed ideals of compact operators), answering questions raised by Guido and Isola.



2007 ◽  
Vol 51 (4) ◽  
pp. 1207-1229 ◽  
Author(s):  
F. Lust-Piquard ◽  
F. Sukochev


Sign in / Sign up

Export Citation Format

Share Document