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- W1973968662 abstract "Kuroda's version of the Weyl-von Neumann theorem asserts that, given any norm ideal [Formula: see text] not contained in the trace class [Formula: see text], every self-adjoint operator A admits the decomposition A=D+K, where D is a self-adjoint diagonal operator and [Formula: see text]. We extend this theorem to the setting of multiplication operators on compact metric spaces (X, d). We show that if μ is a regular Borel measure on X which has a σ-finite one-dimensional Hausdorff measure, then the family {M f :f∈ Lip (X)} of multiplication operators on T 2 (X, μ) can be simultaneously diagonalized modulo any [Formula: see text]. Because the condition [Formula: see text] in general cannot be dropped (Kato-Rosenblum theorem), this establishes a special relation between [Formula: see text] and the one-dimensional Hausdorff measure. The main result of the paper is that such a relation breaks down in Hausdorff dimensions p>1." @default.
- W1973968662 created "2016-06-24" @default.
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- W1973968662 date "2000-11-01" @default.
- W1973968662 modified "2023-09-27" @default.
- W1973968662 title "DIAGONALIZATION MODULO NORM IDEALS AND HAUSDORFF DIMENSIONALITY" @default.
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- W1973968662 doi "https://doi.org/10.1142/s0129167x00000520" @default.
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