J. M. Calabuig

Generalized perfect spaces

Abstract Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Kothe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY). As in the classical case, the containment X ⊂ XYY always holds. We give conditions guaranteeing that X coincides with XYY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in XYY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance.

Vector-valued impact measures and generation of specific indexes for research assessment

A mathematical structure for defining multi-valued bibliometric indices is provided with the aim of measuring the impact of general sources of information others than articles and journals—for example, repositories of datasets. The aim of the model is to use several scalar indices at the same time for giving a measure of the impact of a given source of information, that is, we construct vector valued indices. We use the properties of these vector valued indices in order to give a global answer to the problem of finding the optimal scalar index for measuring a particular aspect of the impact of an information source, depending on the criterion we want to fix for the evaluation of this impact. The main restrictions of our model are (1) it uses finite sets of scalar impact indices (altmetrics), and (2) these indices are assumed to be additive. The optimization procedure for finding the best tool for a fixed criterion is also presented. In particular, we show how to create an impact measure completely adapted to the policy of a specific research institution.

p-variation of vector measures with respect to bilinear maps.

We introduce the spaces V p (X) (resp. V p (X)) of the vector measures F : ! X of bounded (p,B)variation (resp. of bounded (p,B)-semivariation) with respect to a bounded bilinear map B : X◊Y ! Z and show that the spaces L p (X) consisting in functions which are p-integrable with respect to B, defined in [4], are isometrically embedded into V p (X). We characterize V p (X) in terms of bilinear maps from L p 0 ◊ Y into Z and V p B(X) as a subspace of operators from L p 0

Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions

Erdogans work was supported by TUBITAK, the Scientific and Technological Research Council of Turkey. Calabuigs work was supported by Ministerio de Economia, Industria y Competitividad (MINECO) grant MTM2014-53009-P. Sanchez Perezs work was supported by MINECO grant MTM2016-77054-C2-1-P.