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We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. A metric space X is said to have operator norm localization property if there exists 0 < c ≤ 1 such that for every r > 0, there is R > 0 for which, if ν is a positive locally finite Borel measure on X, H is a separable infinite(More)
Impaired sleep patterns are common symptoms of Alzheimer’s disease (AD). Cellular mechanisms underlying sleep disturbance in AD remain largely unknown. Here, using a Drosophila Aβ42 AD model, we show that Aβ42 markedly decreases sleep in a large population, which is accompanied with postdevelopmental axonal arborization of wake-promoting pigment-dispersing(More)
We give some necessary and su‰cient conditions of when the product of two Hankel operators is a compact perturbation of a Hankel operator on the Hardy space. r For f in L y , the Hankel operator with symbol f is the operator H f on the Hardy space H 2 of the unit circle, defined by H f h ¼ PðUf hÞ, for h in H 2. Here P is the orthogonal projection from L 2(More)
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