Geodesic
Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals
Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 67-80

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DOI

We 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 $\phi$ fails the condition that if $x\prec \prec \,Y$ (Hardy-Littlewood-Polya submajorization) and $0\,\le \,x,\,y$ , then $0\,\le \,\phi \left( x \right)\,\le \,\phi \left( y \right)$ . 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.
DOI : 10.4153/CMB-2008-009-3
Mots-clés : 46L52, 47B10, 46E30 
Kalton, Nigel; Sukochev, Fyodor. Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals. Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 67-80. doi: 10.4153/CMB-2008-009-3
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     title = {Rearrangement-Invariant {Functionals} with {Applications} to {Traces} on {Symmetrically} {Normed} {Ideals}},
     journal = {Canadian mathematical bulletin},
     pages = {67--80},
     year = {2008},
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     doi = {10.4153/CMB-2008-009-3},
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