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  • Nilpotent commutators with a masa
    Mastnak, Mitja ; Omladič, Matjaž ; Radjavi, Heydar
    Let ▫$\mathcal{H}$▫ be a complex Hilbert space, let ▫$\mathcal{D} \to \mathcal{B(H)}$▫ ( be a discrete masa (maximal abelian selfadjoint algebra) and let ▫$\mathcal{A}$▫ be a linear subspace (or a ... singleton subset) of ▫$\mathcal{B(H)}$▫ not necessarily having any nontrivial intersection with ▫$\mathcal{D}$▫. Assume that the commutator ▫$AD - DA$▫ is quasinilpotent for every ▫$A \in \mathcal{A}$▫ and every ▫$D \in \mathcal{D}$▫. We prove that ▫$\mathcal{A}$▫ and ▫$\mathcal{D}$▫ are simultaneously triangularizable. If ▫$\mathcal{D}$▫ is a continuous masa, there exist compact operators satisfying this condition that fail to have a multiplicity-free triangularization together with ▫$\mathcal{D}$▫. However, we prove an analogous result in the case where ▫$\mathcal{A}$▫ is a finite-dimensional space of operators of finite rank.
    Vir: Journal of operator theory. - ISSN 0379-4024 (Vol. 74, iss. 2, 2015, str. 371-389)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2015
    Jezik - angleški
    COBISS.SI-ID - 17441881

    Povezava(-e):

    http://dx.doi.org/10.7900/jot.2014jul02.2060

vir: Journal of operator theory. - ISSN 0379-4024 (Vol. 74, iss. 2, 2015, str. 371-389)
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