The dimensions of complemented hilbertian subspaces of uniformly convex Banach lattices
The Distortion of Hilbert Space.
The dual form of the approximation property for a Banach space and a subspace
Given a Banach space X and a subspace Y, the pair (X,Y) is said to have the approximation property (AP) provided there is a net of finite rank bounded linear operators on X all of which leave the subspace Y invariant such that the net converges uniformly on compact subsets of X to the identity operator. In particular, if the pair (X,Y) has the AP then X, Y, and the quotient space X/Y have the classical Grothendieck AP. The main result is an easy to apply dual formulation of this property. Applications...
The dual of the James tree space is asymptotically uniformly convex
The dual of the James tree space is asymptotically uniformly convex.
The exact value of Jung constants in a class of Orlicz function spaces.
Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value:(i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 < CΦ < 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1;(ii) If FΦ(t) is increasing and CΦ > 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1])=2-1/CΦ,where CΦ= limt→+∞ tφ(t)/Φ(t).
The extension of the Krein-Šmulian theorem for order-continuous Banach lattices
If X is a Banach space and C ⊂ X a convex subset, for x** ∈ X** and A ⊂ X** let d(x**,C) = inf||x**-x||: x ∈ C be the distance from x** to C and d̂(A,C) = supd(a,C): a ∈ A. Among other things, we prove that if X is an order-continuous Banach lattice and K is a w*-compact subset of X** we have: (i) and, if K ∩ X is w*-dense in K, then ; (ii) if X fails to have a copy of ℓ₁(ℵ₁), then ; (iii) if X has a 1-symmetric basis, then .
The fixed point property in a Banach space isomorphic to
We consider a Banach space, which comes naturally from and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets.
The fixed point property in Musielak-Orlicz sequence spaces
In this paper, we give necessary and sufficient conditions for a point in a Musielak-Orlicz sequence space equipped with the Orlicz norm to be an H-point. We give necessary and sufficient conditions for a Musielak-Orlicz sequence space equipped with the Orlicz norm to have the Kadec-Klee property, the uniform Kadec-Klee property and to be nearly uniformly convex. We show that a Musielak-Orlicz sequence space equipped with the Orlicz norm has the fixed point property if and only if it is reflexive....
The fixed point property of unital abelian Banach algebras.
The free quasiworld. Freely quasiconformal and related maps in Banach spaces
The Hahn-Banach Theorem surveyed [Book]
The hypo-Euclidean norm of an -tuple of vectors in inner product spaces and applications.
The ideal property of tensor products of Banach lattices with applications to the local structure of spaces of absolutely summing operators
The isomorphic problem of envelopes
The James constant of normalized norms on .
The JNR Property and the Borel Structure of a Banach Space
Research partially supported by a grant of Caja de Ahorros del Mediterraneo.In this paper we study the property of having a countable cover by sets of small local diameter (SLD for short). We show that in the context of Banach spaces (JNR property) it implies that the Banach space is Cech-analytic. We also prove that to have the JNR property, to be σ- fragmentable and to have the same Borel sets for the weak and the norm topologies, they all are topological invariants of the weak topology. Finally, by...
The Joly's construction: A common property of some generalized orthogonalities.
The Krein-Šmulian theorem and its extension
The locally uniform nonsquare in generalized Cesàro sequence spaces.
The mapping in normed linear spaces with applications to inequalities in analysis.