ﻻ يوجد ملخص باللغة العربية
We prove that every Banach space, not necessarily separable, can be isometrically embedded into a $mathcal L_{infty}$-space in a way that the corresponding quotient has the Radon-Nikodym and the Schur properties. As a consequence, we obtain $mathcal L_infty$ spaces of arbitrary large densities with the Schur and the Radon-Nikodym properties. This extents the a classical result by J. Bourgain and G. Pisier.
We develop a novel and unifying setting for phase retrieval problems that works in Banach spaces and for continuous frames and consider the questions of uniqueness and stability of the reconstruction from phaseless measurements. Our main result state
We develop a discrete framework for the interpolation of Banach spaces, which contains e.g. the well-known real and complex interpolation methods, but also more exotic methods like the $pm$-method, the Radamacher interpolation method and the $ell^p$-
We introduce the class of slicely countably determined Banach spaces which contains in particular all spaces with the RNP and all spaces without copies of $ell_1$. We present many examples and several properties of this class. We give some applicatio
We prove that every isometry between two combinatorial spaces is determined by a permutation of the canonical unit basis combined with a change of signs. As a consequence, we show that in the case of Schreier spaces, all the isometries are given by a
Assume that $mathcal{I}$ is an ideal on $mathbb{N}$, and $sum_n x_n$ is a divergent series in a Banach space $X$. We study the Baire category, and the measure of the set $A(mathcal{I}):=left{t in {0,1}^{mathbb{N}} colon sum_n t(n)x_n textrm{ is } mat