Related papers: Unconditional basic sequences in function spaces w…

The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c, the Banach space of null sequences under…

Let $M$ be a non-degenerate Orlicz function such that there exist $\ep > 0$ and $0 < s < 1$ with $\su M(\ep s^i)/M(s^i) < \infty$. It is shown that the Orlicz sequence space $h_M$ is isomorphic to a subspace of $C(\om^\om)$. It is also…

We exhibit the necessary range for which functions in the Sobolev spaces $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle-Lemari\'e wavelets. We also consider the natural…

We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the unit vector basis of $l_1$. We show that a normalized unconditional basic sequence…

In this paper, we study spaceability of subsets of generalized Orlicz and Lebesgue spaces associated to Banach function space. Also, we give some sufficient conditions for spaceability of subsets of a general Banach space which improves an…

We study the problem of the existence of unconditional basic sequences in Banach spaces of high density. We show, in particular, the relative consistency with GCH of the statement that every Banach space of density $\aleph_\omega$ contains…

A reflexive Banach space with an unconditional basis admits an equivalent $1$-unconditional $2R$ norm and embeds into a reflexive space with a $1$-symmetric $2R$ norm. Partial results on $1$-symmetric $2R$ renormings of spaces with a…

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…

We study Banach spaces X with a strongly asymptotic l_p basis (any disjointly supported finite set of vectors far enough out with respect to the basis behaves like l_p) which are minimal (X embeds into every infinite dimensional subspace).…

In this paper, we study the noncommutative Orlicz space $L_{\varphi}(\widetilde{\mathcal{M}},\tau)$, which generalizes the concept of noncommutative $L^{p}$ space, where $\mathcal{M}$ is a von Neumann algebra, and $\varphi$ is an Orlicz…

S. Banach, in particular, proved that for any function, even $f(x) = 1,$ where $x\in[0,1],$ the convergence of its Fourier series with respect to the general orthonormal systems (ONS) is not guaranteed. In this paper, we find conditions for…

For a large class of Banach spaces, a general construction of subspaces without local unconditional structure is presented. As an application it is shown that every Banach space of finite cotype contains either $l_2$ or a subspace without…

We prove that $L_2(\mathbb{R})$ contains a Schauder basis of non-negative functions. Similarly, $L_p(\mathbb{R})$ contains a Schauder basic sequence of non-negative functions such that $L_p(\mathbb{R})$ embeds into the closed span of the…

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…

We study Orlicz functions that do not satisfy the $\Delta_2$-condition at zero. We prove that for every Orlicz function $M$ such that $\limsup_{t\to0}M(t)/t^p >0$ for some $p\ge1$, there exists a positive sequence $T=(t_k)_{k=1}^\infty$…

Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes of) p-integrable functions on [0,1]. It is known that a sequence of independent copies of a mean zero random variable f from L_p spans in L_p a subspace…

A generalization of Lozanovskii's result is proved. Let E be $k$-dimensional subspace of an $n$-dimensional Banach space with unconditional basis. Then there exist $x_1,..,x_k \subset E$ such that $B_E \p \subset \p absconv\{x_1,..,x_k\}$…

Let $X$ be a Banach space with an unconditional finite-dimensional Schauder decomposition $(E_n)$. We consider the general problem of characterizing conditions under which one can construct an unconditional basis for $X$ by forming an…

Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2.

Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-K\"{o}the spaces, then there exists a…