If X is a closed subspace of a Banach space L which embeds into a Banach lattice not containing l ∞ ’s uniformly and L/X contains l ∞ ’s uniformly, then X cannot have local unconditional structure in the sense of Gordon-Lewis (GLl.u.st.). 1991 Mathematics Subject Classification. 46B03, 43A46.

It is pointed out that the method used by L. Carleson to study interpolation by bounded analytic functions applies to the study of the analogous problem for H" functions. In particular, there exist sequences of points in the unit disc which are not uniformly separated, but which are such that every l" sequence can be interpolated along this sequence by an Hv function (l^p^q^ + oo). Let (77", /"...

Article history: Received 2 April 2014 Available online 2 July 2014 Submitted by P. Nevai

‎In this paper‎, ‎we define and study the notion of zero elements in topoframes; a topoframe is a pair‎ ‎$(L‎, ‎tau)$‎, ‎abbreviated $L_{ tau}$‎, ‎consisting of a frame $L$ and a‎ ‎subframe $ tau $ all of whose elements are complemented elements in‎ ‎$L$‎. ‎We show that‎ ‎the $f$-ring $ mathcal{R}(L_tau)$‎, ‎the set of $tau$-real continuous functions on $L$‎, ‎is uniformly complete‎. ‎Also‎, ‎t...

Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space X means that, for every element u in the ...

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

Let $$L(t) = - \mathrm{div} \left( A(x,t) \nabla _x \right) $$ for $$t \in (0, \tau )$$ be a uniformly elliptic operator with boundary conditions on domain $$\Omega of $$\mathbb {R}^d$$ and $$\partial \frac{\partial }{\partial t}$$ . Define the parabolic $${{\mathcal {L}}}= \partial + L$$ $$L^2(0, , L^2(\Omega ))$$ by $$({{\mathcal {L}}}u)(t) := u(t)}{\partial t} L(t)u(t)$$ We assume very littl...

We construct a uniformly bounded orthonormal almost greedy basis for L p ([0, 1]), 1 < p < ∞. The example shows that it is not possible to extend Orlicz's theorem, stating that there are no uniformly bounded orthonormal unconditional bases for L p ([0, 1]), p = 2, to the class of almost greedy bases.

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.