Marco Thill
We give an elementary proof of a monotone selection principle which allows to pass from increasing nets to increasing sequences in the Hermitian part of a $σ$-finite von Neumann algebra. This is to be seen as a ``monotone version'' of first countability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We prove in an elementary fashion that the image of a commutative monotone $σ$-complete $C^*$-algebra under a $σ$-normal morphism is again monotone $σ$-complete and give an application of this result in spectral theory.
In a central lemma we characterize "generating functions" of certain functors on the category of algebraic non-commutative probability spaces. Special families of such generating functions correspond to "unital, associative universal products" on this category, which again define a notion of non-commutative stochastic independence. Using the central lemma, we can prove the existence of cumulants and of "cumulant Lie-algebras" for a wide class of independences. These include the five independences (tensor, free, Boolean, monotone, anti-monotone) appearing in N. Murakis classification, c-free in…
We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice properties on one dimensional slices. Let $E \subset \mathbb{R}^d$ be open. A function $f:E \to \mathbb{R}$ is matrix monotone lite if $f(φ_1(t), \ldots, φ_d(t))$ is a matrix monotone function of $t$ whenever $t \in (0,1)$, the $φ_i$ are automorphisms of the upper half plane, and the tuple $(φ_1(t), \ldots, φ_d(t))$ maps $(0,1)$ into $E$. We use the "royal road"…
We apply to operator algebra theory a monotone selection principle which apparently escaped attention (of operator algebra theorists) so far. This principle relates to the basic order theoretic characterisation of von Neumann algebras given by Kadison, and the simplified form this result takes in separable Hilbert spaces. In the separable case we need only consider increasing sequences rather than increasing nets. We apply an argument of Klaus Floret to show that, within the realm of commutativity, there exists a general monotone selection principle providing for this simplification. Thereby w…
We introduce and study a new notion of non-commutative independence, called V-monotone independence, which can be viewed as an extension of the monotone independence of Muraki. We investigate the combinatorics of mixed moments of V-monotone random variables and prove the central limit theorem. We obtain a combinatorial formula for the limit moments and we find the solution of the differential equation for the moment generating function in the implicit form.
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean convolution of probability measures on the positive half-line is proposed. Unlike Bercovici's multiplicative boolean convolution it is always defined, but it turns out to be neither commutative nor associative. Finally some relations between free, monotone, and boolean convolutions are discussed.
Representation formulas for faces and support functions of the values of maximal monotone operators are established in two cases: either the operators are defined on uniformly Banach spaces with uniformly convex duals, or their domains have nonempty interiors on reflexive real Banach spaces. Faces and support functions are characterized by the limit values of the minimal-norm selections of maximal monotone operators in the first case while in the second case they are represented by the limit values of any selection of maximal monotone operators. These obtained formulas are applied to study the…
In this paper we establish a multivariable non-commutative generalization of Löwner's classical theorem from 1934 characterizing operator monotone functions as real functions admitting analytic continuation mapping the upper complex half-plane into itself. The non-commutative several variable theorem proved here characterizes several variable operator monotone functions, not assumed to be free analytic or even continuous, as free functions that admit free analytic continuation mapping the upper operator poly-halfspace into the upper operator halfspace over an arbitrary Hilbert space. We establ…
Alternating Weighted Residual Flows and the Non-Commutative Gap
本文提出了一种非线性交替加权残差流方法，用于分析非交换算子的极限行为，并揭示其与经典短算子之间的关系。
Law of large numbers for non-linear traces of the Choquet type on finite factors
本文研究有限因子上的Choquet型非线性迹的大数定律，通过估计聚点范围（上/下极限）处理非收敛性，并发现满足均匀范数大数定律的Powers二元移位例子，推进了非线性非交换概率论。
An operator convex function on (0,\infty) which satisfies the symmetry condition k(1/x) = x k(x) can be used to define a type of non-commutative multiplication by a positive definite matrix (or its inverse) using the primitive concepts of left and right multiplication and the functional calculus. The operators for the inverse can be used to define quadratic forms associated with Riemannian metrics which contract under the action of completely positive trace-preserving maps. We study the question of when these operators define maps which are also completely positive (CP). Although A --> D^{-1/2…
Frame expansions with erasures: an approach through the non-commutative operator theory
本文证明任意n维框架在随机系数丢失下，可从(n log n)个随机系数高概率线性重建信源，优于正交基，证明基于非交换算子理论。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。