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- W2000727902 abstract "Let Ai,Bi, and Xi, i=1,…,n, be bounded linear operators on a separable Hilbert space such that Xi is compact for i=1,…,n. It is shown that the singular values of ∑i=1nAiXiBi are dominated by those of ∑i=1n‖Ai‖‖Bi‖(⊕i=1nXi), where ‖·‖ is the usual operator norm. Among other applications of this inequality, we prove that if A and B are self-adjoint operators such that a1⩽A⩽a2 and b1⩽B⩽b2 for some real numbers a1,a2,b1, and b2, and if X is compact, then the singular values of the generalized commutator AX-XB are dominated by those of max(b2-a1,a2-b1)(X⊕X). This inequality proves a recent conjecture concerning the singular values of commutators. Several inequalities for norms of commutators are also given." @default.
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- W2000727902 date "2010-02-01" @default.
- W2000727902 modified "2023-09-25" @default.
- W2000727902 title "Singular values, norms, and commutators" @default.
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- W2000727902 doi "https://doi.org/10.1016/j.laa.2009.10.042" @default.
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