5,326 research outputs found

    Multiplicativity properties of entrywise positive maps

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    Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that the entries of a matrix representative of the map are non-negative (EP). In particular, for integer t, multiplicativity holds for the maximal 2 -> 2t norm of a product of two maps, whenever one of the pair is EP; for the maximal 1 -> t norm for pairs of CP maps when one of them is also EP; and for the maximal 1 -> 2t norm for the product of an EP and a 2-positive map. Similar results are shown in the infinite-dimensional setting of convolution operators on L^2(R), with the pointwise positivity of an integral kernel replacing entrywise positivity of a matrix. These results apply in particular to Gaussian bosonic channels.Comment: results extended to some infinite dimensional cases, including the Gaussian bosonic channe

    Welfare and Work in the 1990s: Experiences in Six Cities

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    Our study examines the dynamic structure of welfare participation and the labor market involvement of recipients starting in the early 1990s and extending through 1999 in the core counties containing six major urban areas: Atlanta, Baltimore, Chicago, Fort Lauderdale, Houston, and Kansas City. By focusing on six major cities, we can examine the extent to which differences in state and local policy, administrative directives, and local labor market conditions contribute to observed trends.Welfare Reform
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