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

Canadian mathematical bulletin

关键词: isoperimetric functions;    Dehn functions;    hyperbolic groups;   

DOI  :  10.4153/CMB-2008-009-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We present a construction of singular rearrangementinvariant functionals on Marcinkiewicz function/operator spaces.The functionals constructed differ from all previous examples inthe literature in that they fail to be symmetric. In other words,the functional $phi$ fails the condition that if $xpprec y$(Hardy-Littlewood-Polya submajorization) and $0leq x,y$, then$0le phi(x)le phi(y).$ We apply our results to singular traceson symmetric operator spaces (in particular onsymmetrically-normed ideals of compact operators), answeringquestions raised by Guido and Isola.

【 授权许可】

Unknown