Related papers: On M-ideals and o-O type spaces

A number of Calder\'on-Mityagin couples and relative Calder\'on-Mityagin pairs are identified among Banach function spaces defined in terms of the least decreasing majorant construction on the half line. The interpolation structure of such…

We study Banach spaces whose group of isometries acts micro-transitively on the unit sphere. We introduce a weaker property, which one-complemented subspaces inherit, that we call uniform micro-semitransitivity. We prove a number of results…

It is shown that every set I(m) of Banach lattices of measurable functions defined on a measure space (Q,S,m), equipped with a some natural ordering became a modular lattice, which is Dedekind complete provided m is a probability measure.…

Given any Banach space $X$, let $L_2^X$ denote the Banach space of all measurable functions $f:[0,1]\to X$ for which ||f||_2:=(int_0^1 ||f(t)||^2 dt)^{1/2} is finite. We show that $X$ is a UMD--space (see \cite{BUR:1986}) if and only if…

In this paper, we first study the bounded mean oscillation of planar harmonic mappings, then a relationship between Lipschitz-type spaces and equivalent modulus of real harmonic mappings is established. At last, we obtain sharp estimates on…

We study the predual of the space of functions of bounded variation defined over a metric measure space $({\rm X},{\sf d},\mathfrak m)$ with $\mathfrak m$ finite. More specifically, for any exponent $p\in(1,\infty)$ we construct an…

Nonreflexive Banach spaces that are complemented in their bidual by an L-projection - like preduals of von Neumann algebras or the Hardy space $H^1$ - contain, roughly speaking, many copies of $l^1$ which are very close to isometric copies.…

We study the spectrum $M_b(U)$ of the algebra of bounded type holomorphic functions on a complete Reinhardt domain in a symmetrically regular Banach space $E$ as an analytic manifold over the bidual of the space. In the case that $U$ is the…

The spaces $W_\alpha$ are the Banach spaces whose duals are isometric to $\ell_1$ and such that the standard basis of $\ell_1$ is $w^*$-convergent to $\alpha\in \ell_1$. The core result of our paper proves that an $\ell_1$-predual $X$…

In this article we extend recent results by the first author on the necessity of $BMO$ for the boundedness of commutators on the classical Lebesgue spaces. We generalize these results to a large class of Banach function spaces. We show that…

For a certain class of algebras $\cal A$ we give a method for constructing Banach spaces $X$ such that every operator on $X$ is close to an operator in $\cal A$. This is used to produce spaces with a small amount of structure. We present…

We study the Daugavet property in the space of Lipschitz functions $\operatorname{Lip}_0(M)$ for a complete metric space $M$. Namely we show that $\operatorname{Lip}_0(M)$ has the Daugavet property if and only if $M$ is a length space. This…

We give a characterization of the existence of copies of $c_{0}$ in Banach spaces in terms of indexes. As an application, we deduce new proofs of James Distortion theorem and Bessaga-Pe{\l}czynski theorem about weakly unconditionally Cauchy…

We prove that for certain subsets $M \subseteq \mathbb{R}^N$, $N \geqslant 1$, the Lipschitz-free space $\mathcal{F}(M)$ has the metric approximation property (MAP), with respect to any norm on $\mathbb{R}^N$. In particular,…

We define a scale of L^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John-Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition…

We characterize preduals and K\"othe duals to a class of Sobolev multiplier type spaces. Our results fit in well with the modern theory of function spaces of harmonic analysis and are also applicable to nonlinear partial differential…

Let $(\mathcal{X}, d, \mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\Phi$ a concave function on $(0,\infty)$ of critical lower type…

In [8] probabilistic methods, in particular a variant of the Weak Law of Large Numbers related to the Bernoulli distribution, have been used to show that for every infinite compact spaces K and L there exists a sequence $(\mu_n)$ of…

In the paper we introduce Orlicz type functional spaces defined in terms of nonlocal convolution type integral functionals and study the main properties of these spaces. We show in particular that, under natural convexity and growth…

Given a fully symmetric Banach function space $E$ and a decreasing positive weight $w$ on $I = (0, a)$, $0 < a \le \infty $, the generalized Lorentz space ${\Lambda}_{E,w}$ is defined as the symmetrization of the canonical copy $E_w$ of $E$…