Produits tensoriels d'espaces de Banach et classes d'applications linéaires
Produits tensoriels et , applications -sommantes, applications -radonifiantes
Produits tensoriels injectifs d'espaces de Sidon
Projections contractantes dans
Projections contractantes dans les espaces de Banach
Projections de meilleure approximation continues dans certains espaces de Banach
Projections from a von Neumann algebra onto a subalgebra
Projections from onto
Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let and be Banach spaces such that is weakly compactly generated Asplund space and has the approximation property (respectively is weakly compactly generated Asplund space and has the approximation property). Suppose that and let . Then (respectively ) can be equivalently renormed so that any projection of onto has the sup-norm greater or equal to .
Projections in dual weakly compactly generated Banach spaces
Projections on Banach spaces with symmetric bases
Projections onto the spaces of Toeplitz operators
Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.
Projections, skewness and related constants in real normed spaces.
Projetive generators and resolutions of identity in Banach spaces.
We introduce the notion of projective generator on a given Banach space. Weakly countably determined and dual spaces with the Radon Nikodým property have projective generators. If a Banach space has projective generator, then it admits a projective resolution of the identity. When a Banach space and its dual both have a projective generator then the space admits a shrinking resolution of the identity. These results include previous ones of Amir and Lindenstrauss, John and Zizler, Gul?ko, Vaak, Tacon,...
Proper subspaces and compatibility
Let 𝓔 be a Banach space contained in a Hilbert space 𝓛. Assume that the inclusion is continuous with dense range. Following the terminology of Gohberg and Zambickiĭ, we say that a bounded operator on 𝓔 is a proper operator if it admits an adjoint with respect to the inner product of 𝓛. A proper operator which is self-adjoint with respect to the inner product of 𝓛 is called symmetrizable. By a proper subspace 𝓢 we mean a closed subspace of 𝓔 which is the range of a proper projection. Furthermore,...
Proper uniform algebras are flat
In this brief note, we see that if is a proper uniform algebra on a compact Hausdorff space , then is flat.
Properly semi-L-embedded complex spaces
We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.
Properties and applications of Tauberian operators.
Tauberian operators, which appeared in response to a problem in summability [GaW, KW] have found application in several situations: factorization of operators [DFJP], preservation of isomorphic properties of Banach spaces [N, NR], equivalence between the Radon-Nikodym property and the Krein-Milman property [Sch], and generalized Fredholm operators [Ta, Y].This paper is a survey of the main properties and applications of Tauberian operators.
Properties of intersection in the geometry of sequences in Banach spaces.
Properties of lush spaces and applications to Banach spaces with numerical index 1
The concept of lushness, introduced recently, is a Banach space property, which ensures that the space has numerical index 1. We prove that for Asplund spaces lushness is actually equivalent to having numerical index 1. We prove that every separable Banach space containing an isomorphic copy of c₀ can be renormed equivalently to be lush, and thus to have numerical index 1. The rest of the paper is devoted to the study of lushness just as a property of Banach spaces. We prove that lushness is separably...
Properties of Sequence Spaces in Which l1 is Weakly Compactly Embedded.