具有性质 (A) 的条件基

条件期望算子的不交型性质

A disjointness type property of conditional expectation operators

通过一个类似于保带算子的不交性性质，给出了条件期望算子的一个刻画。我们说巴拿赫格$X$上的算子$T:X\to X$是半带保持的当且仅当对所有的$f, g \in X$，$f \perp Tg$蕴涵$Tf \perp Tg$ .证明了当$X$是纯原子巴拿赫格时，$X$上的算子$T$是加权条件期望算子当且仅当$T$是半带保持的.

A conditional construction of restricted isometries

We study the restricted isometry property of a matrix that is built from the discrete Fourier transform matrix by collecting rows indexed by quadratic residues. We find an $ε>0$ such that, conditioned on a folklore conjecture in number theory, this matrix satisfies the restricted isometry property with sparsity parameter $K=Ω(M^{1/2+ε})$, where $M$ is the number of rows.

Convergence theorems for barycentric maps

We first develop a theory of conditional expectations for random variables with values in a complete metric space $M$ equipped with a contractive barycentric map $β$, and then give convergence theorems for martingales of $β$-conditional expectations. We give the Birkhoff ergodic theorem for $β$-values of ergodic empirical measures and provide a description of the ergodic limit function in terms of the $β$-conditional expectation. Moreover, we prove the continuity property of the ergodic limit function by finding a complete metric between contractive barycentric maps on the Wasserstein space of…

通过切线过程尾估计刻画UMD性质

Characterizations of the UMD property via tail estimates for tangent processes

本文通过切线条件对称过程的尾界刻画Banach空间的UMD性质，证明了UMD等价于某种尾估计成立，同时推导了相关的洛伦茨范数不等式及离散、连续和纯离散情形的刻画。

The Topology of Information on the Space of Probability Measures over Polish Spaces

We study here the topology of information on the space of probability measures over Polish spaces that was defined in [1]. We show that under this topology, a convergent sequence of probability measures satisfying a conditional independence property converges to a measure that also satisfies the same conditional independence property. In the process of showing this, we also provide a correct proof of the result in Lemma 4 in [1].