For each natural number N, we give an example of a Banach space X such that the set norm attaining N-linear forms is dense in all continuous on X, but there are (N+1)-linear which cannot be approximated

We investigate in this paper the complementation of copies $c_0(I)$ some classes Banach spaces (in class weakly compactly generated (WCG) spaces, larger $\mathcal{V}$ which are subspaces $C(K)$ space with $K$ a Valdivia compact, and $C([1, \alpha ])$, where $\alpha$ is an ordinal) embedding elements $\mathcal{C}$ complemented spaces. Two our results as follows: (i) $X \in \mathcal{V}$ every copy $\# I < \aleph _{\omega}$ complemented; (ii) if $\alpha _0 = _0$, _{n+1} 2^{\alpha _n}$, $n...

We are concerned in this paper with the density of functionals which do not attain their norms Banach spaces. Some earlier results given for separable spaces extended to nonseparable case. obtain that a space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is reflexive if and...

We introduce and study the Kunen&#8211;Shelah properties ${\rm KS}_i$, $ i=0,1,\ldots ,7$. Let us highlight some of our results for a Banach space $X$: (1)&nbsp;$X^*$ has $w^*$-nonseparable equivalent dual ball iff $X$ an $\omega$-<i>polyhedron</

We study the size of range derivatives a smooth function between Banach spaces. establish conditions on pair spaces $X$ and $Y$ to ensure existence $C^p$ (Fréchet or continuous Gâteaux smooth) $f$ from onto such that vanishes outside bounded set all are surjections. In particular we deduce following results. For case, when separable is infinite-dimensional, there exists $Y$, with support, so $f^{\prime}(X) = {\cal L}(X,Y)$. Fréchet get if space has bump ${\rm dens} X {\rm L}(X,Y)$, then $f:...

Let ℳ be the collection of all intersections balls, considered as a subset hyperspace closed, convex and bounded sets Banach space, furnished with Hausdorff metric. It is proved that uniformly very porous if only space fails Mazur intersection property.

This paper presents a study of some elastic properties the projections using Second Order Theory Chovitz. results in new azimuthal projection which yields minimum deformation energy.The application strain criteria map has been proposed by Dermanis et al. Since this approach gives cumbersome formulae second order Chovitz theory is used to facilitate study. sufficient for most small scale applications.At same time difference between direct and obtained studied.

Part 1 of this paper was published in the preceeding issue journal (34, 271 January 1999)

We study the size of sets gradients bump functions on Hilbert space ℓ 2 , and related question as to how small set tangent hyperplanes a smooth bounded starlike body in can be. find that those be quite small. On one hand, usual norm uniformly approximated by C 1 Lipschitz ψ so cones generated ranges its derivatives ' (ℓ ) have empty interior. This implies there are bumps their other we construct -smooth bodies A⊂ℓ which approximate unit ball, A interior well. also explain why this is best...

It is proved that the dual of a Banach space with Mazur intersection property almost weak* Asplund. Analogously, predual Through use these arguments, it found that, in particular, all (in Baire sense) equivalent norms on l1(Γ) and l∞(Γ) are Fréchet differentiable dense Gδ subset. Necessary conditions for properties terms convex sets satisfying Krein–Milman type condition also discussed. shown if has property, then every subspace countable codimension can be equivalently renormed to satisfy...

Abstract We establish sufficient conditions on the shape of a set A included in space ( X , Y ) n -linear symmetric mappings between Banach spaces and to ensure existence C -smooth mapping f : → with bounded support, such that = provided admits bump -th derivative dens ℒ ). For instance, when is infinite-dimensional, every connected open U containing origin range amapping. The same holds true for closure point boundary end path within . In finite-dimensional case, more restrictive are...