Practical and theoretical aspects of CdSe-CdS heterojunctions

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Spear operators between Banach spaces

The aim of this manuscript is to study \emph{spear operators}: bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that $$\|G + \omega\,T\|=1+ \|T\|.$$ To this end, we introduce two related properties, one weaker called the alternative Daugavet property (if rank-one operators $T$ satisfy the requirements), and one stronger called lushness, and we develop a complete theory about the relations between these three properties. To do this, the concepts of spear vector and spear set play an important role. Further, we provide with many examples among classical spaces, being one of them the lushness of the Fourier transform on $L_1$. We also study the relation of these properties with the Radon-Nikod\'ym property, with Asplund spaces, with the duality, and we provide some stability results. Further, we present some isometric and isomorphic consequences of these properties as, for instance, that $\ell_1$ is contained in the dual of the domain of every real operator with infinite rank and the alternative Daugavet property, and that these three concepts behave badly with smoothness and rotundity. Finally, we study Lipschitz spear operators (that is, those Lipschitz operators satisfying the Lipschitz version of the equation above) and prove that (linear) lush operators are Lipschitz spear operators.Comment: 114 pages, 9 chapter

Measuring inequality in a region: a SAM approach

In this paper, we apply SAM linear models to the economy in a Spanish region, Extremadura, from the usual household disaggregation of these matrices. The analysis aims to some issues related to income distribution. To achieve these goals, some relative multipliers are computed and we propose different simulations based on final demand and income transfers. Finally, we also compute the standard statistical measures of inequality and show how these measures change if different transfer policies are applied. JEL CODES: C69, D31, D59, H59