In the context of vector-valued extensions of variational principles we are dealing with functions taking values in a Banach space partially ordered by a closed convex pointed cone. We introduce and study a new notion of semi-continuity connected with the order and we improve the vector-valued extensions of Deville-Godefroy-Zizler perturbed minimization… (More)
We study the numerical index of a Banach space from the isomor-phic point of view, that is, we investigate the values of the numerical index which can be obtained by renorming the space. The set of these values is always an interval which contains [0, 1/3[ in the real case and [e −1 , 1/2[ in the complex case. Moreover, for " most " Banach spaces the least… (More)
We give a new vector-valued extension of Deville-Godefroy-Zizler perturbed minimization principle. The functions we are considering are taking values in a real Banach space partially ordered by a closed convex pointed cone.
We study the composition operators on an algebra of Dirichlet series, the analogue of the Wiener algebra of absolutely convergent Taylor series , which we call the Wiener-Dirichlet algebra, namely the connection between the properties of the operator and of its symbol, with special emphasis on the compact, automorphic, or isometric character of this… (More)
This paper is a short survey on the numerical range of some composition operators. The first part is devoted to composition operators on the Hilbert Hardy space H 2 on the unit disk. The results are due to P. In the second part we study the numerical range of composition operators on the Hilbert space H 2 of Dirichlet series. These results are due to H.… (More)
We prove that every M-ideal is strongly proximinal and that, for any Banach space X, K(X, c 0) is an M-ideal in L(X, ∞). 1 2-ball property, compact operators. * The authors want to thank the " Banque Nationale de Belgique " for the grant they got.