Rearrangement-Invariant Functionals with Applications to Traces on Symmetrically Normed Ideals

Kalton, Nigel ; Sukochev, Fyodor

Canadian mathematical bulletin, Tome 51 (2008) no. 1, pp. 67-80

Résumé

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.

Détail

DOI : 10.4153/CMB-2008-009-3

Mots-clés : 46L52, 47B10, 46E30

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