On Fourier series in eigenfunctions of elliptic boundary value problems.
On Fréchet differentiability of convex functions on Banach spaces
Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function defined on a separable Banach space are studied. The conditions are in terms of a majorization of by a -smooth function, separability of the boundary for or an approximation of by Fréchet smooth convex functions.
On Gaps Between Bounded Operators
On Gateaux differentiable bump functions
It is shown that the order of Gateaux smoothness of bump functions on a wide class of Banach spaces with unconditional basis is not better than that of Fréchet differentiability. It is proved as well that in the separable case this order for Banach lattices satisfying a lower p-estimate for 1≤ p < 2 can be only slightly better.
On generalized Bergman spaces
Let D be the open unit disc and μ a positive bounded measure on [0,1]. Extending results of Mateljević/Pavlović and Shields/Williams we give Banach-space descriptions of the classes of all harmonic (holomorphic) functions f: D → ℂ satisfying .
On Grothendieck spaces of type C(K)
On Hamel bases in Banach spaces
It is shown that no infinite-dimensional Banach space can have a weakly K-analytic Hamel basis. As consequences, (i) no infinite-dimensional weakly analytic separable Banach space E has a Hamel basis C-embedded in E(weak), and (ii) no infinite-dimensional Banach space has a weakly pseudocompact Hamel basis. Among other results, it is also shown that there exist noncomplete normed barrelled spaces with closed discrete Hamel bases of arbitrarily large cardinality.
On having a countable cover by sets of small local diameter
A characterization of topological spaces admitting a countable cover by sets of small local diameter close in spirit to known characterizations of fragmentability is obtained. It is proved that if X and Y are Hausdorff compacta such that C(X) has an equivalent p-Kadec norm and has a countable cover by sets of small local norm diameter, then has a countable cover by sets of small local norm diameter as well.
On Hilbert sets and -spaces with no subspace isomorphic to
On Hilbert-Schmidt spaces
On inclusion relations between Lorentz sequence spaces and inequalities of Lewis type.
On Incomparability of Banach Spaces.
On incomparability of Banach spaces
Several concepts of incomparability of Banach spaces have been considered in the literature, which allow one to describe some of the properties of the product of two Banach spaces as a juxtaposition of the corresponding properties of the factors. In this paper we study the relations between these concepts of incomparability, survey the main results and applications, and state some open problems.
On incomparability of Banach spaces.
On Inductive Limits of Banach Spaces.
On infinite dimensional uniform smoothness of Banach spaces
An infinite dimensional counterpart of uniform smoothness is studied. It does not imply reflexivity, but we prove that it gives some -type estimates for finite dimensional decompositions, weak Banach-Saks property and the weak fixed point property.
On integral transforms of Haar functions
On integration in Banach spaces, I
On interpolation of bilinear operators by methods associated to polygons
Stabiliamo teoremi di interpolazione bilineare per una combinazione dei metodi di - e -interpolazione associati ai poligoni, e per il -metodo. Mostriamo che un simile risultato fallisce per il -metodo, e diamo applicazioni all'interpolazione di spazi di operatori.
On interpolation of tensor products of Banach spaces.
For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.