Darstellung von Banach-Verbänden und Sätze vom Korovkin-Typ.
Das Spektrum von Verbandsoperatoren in Banachverbänden.
Daugavet centers and direct sums of Banach spaces
A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center...
De la recherche pétrolière à la géométrie des espaces de Banach en passant par les paraproduits
De nouveaux espaces de Banach sans la propriété d'approximation
Decomposable subspaces of Banach spaces.
We introduce and study the notion of hereditarily A-indecomposable Banach space for A a space ideal. For a hereditarily A-indecomposable space X we show that the operators from X into a Banach space Y can be written as the union of two sets A Φ+(X,Y) and A(X;Y ). For some ideals A defined in terms of incomparability, the first set is open, the second set correspond to a closed operator ideal and the union is disjoint.
Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps
* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis. If a Banach space E cannot...
Decompositions for real Banach spaces with small spaces of operators
We consider real Banach spaces X for which the quotient algebra (X)/ℐn(X) is finite-dimensional, where ℐn(X) stands for the ideal of inessential operators on X. We show that these spaces admit a decomposition as a finite direct sum of indecomposable subspaces for which is isomorphic as a real algebra to either the real numbers ℝ, the complex numbers ℂ, or the quaternion numbers ℍ. Moreover, the set of subspaces can be divided into subsets in such a way that if and are in different subsets,...
Deformation of Banach spaces
Using some moduli of convexity and smoothness we introduce a function which allows us to measure the deformation of Banach spaces. A few properties of this function are derived and its applicability in the geometric theory of Banach spaces is indicated.
Degree of convexity and product spaces
Demand continuity and equilibrium in Banach commodity spaces
Norm-to-weak* continuity of excess demand as a function of prices is proved by using our two-topology variant of Berge's Maximum Theorem. This improves significantly upon an earlier result that, with the extremely strong finite topology on the price space, is of limited interest, except as a vehicle for proving equilibrium existence. With the norm topology on the price space, our demand continuity result becomes useful in applications of equilibrium theory, especially to problems with continuous...
Denjoy integral and Henstock-Kurzweil integral in vector lattices. I
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.
Denjoy integral and Henstock-Kurzweil integral in vector lattices. II
In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.
Dense Hyperplanes of First Category.
Dense strong continuity of mappings and the Radon-Nikodym property.
Denseness of norm attaining mappings.
The Bishop-Phelps Theorem states that the set of (bounded and linear) functionals on a Banach space that attain their norms is dense in the dual. In the complex case, Lomonosov proved that there may be a closed, convex and bounded subset C of a Banach space such that the set of functionals whose maximum modulus is attained on C is not dense in the dual. This paper contains a survey of versions for operators, multilinear forms and polynomials of the Bishop-Phelps Theorem. Lindenstrauss provided examples...
Dentabilité et points extrémaux
Dentability and finite-dimensional decompositions
Denting point in the space of operator-valued continuous maps.
In a former paper we describe the geometric properties of the space of continuous functions with values in the space of operators acting on a Hilbert space. In particular we show that dent B(L(H)) = ext B(L(H)) if dim H < 8 and card K < 8 and dent B(L(H)) = 0 if dim H < 8 or card K = 8, and x-ext C(K,L(H)) = ext C(K,L(H)).
Denting points in Bochner Banach ideal spaces .