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Let μ, μ′, v, v’ denote σ-finite measures on certain measurable spaces, let 1 ≤ q,p ≤ ∞, and let S : Lp(μ) → Lq(μ′), T: Lp(v) → Lq(v’) be given bounded linear operators. It is proved that if q < p, then (in general) S ⊗ T extends to a bounded linear operator U...
One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to represent such subjective assessments and to process them by analyzing, quantifying and identifying the inconsistencies. We propose using smaller scales for pairwise comparisons and provide mathematical and practical justifications...
King and Ruskai asked whether the norm of a completely positive map acting between Schatten classes of operators is equal to that of its restriction to the real subspace of self-adjoint operators. Proofs have been promptly supplied by Watrous and Audenaert. Here we provide one more proof, in fact of a slightly more general fact, under the (slightly weaker) assumption of 2-positivity. The argument...
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