Generalization of some commutative perturbation results

A Generalization of Gajda's Equation on Commutative Topological Groups

In the present paper we deal with the following generalization of the sine-cosine equation \begin{equation*} \int f_1(x+y-t)+f_2(x-y+t) dμ(t)=g(x)h(y) \end{equation*} for complex valued functions $f_1$, $f_2$, $g$ and $h$ defined on a commutative topological group $G$, where $μ$ is a complex measure defined on $G$.

Perturbations not necessarily commutative

This paper treatises the preservation of some spectra under perturbations not necessarily commutative and generalizes several results which have been proved in the case of commuting operators.

算子的扰动与非交换凝聚器：关于拟中心模数的最新进展

Perturbations of operators and non-commutative condensers, an update on the quasicentral modulus

本文综述了拟中心模数这一算子不变量在扰动理论、分形测度及动力学熵中的关键作用，并介绍了新兴的非交换凝聚器容量类比，为相关研究提供新视角。

Interpolation Between $H^p$ Spaces and Non-Commutative Generalizations II

We continue an investigation started in a preceding paper. We discuss the classical results of Carleson connecting Carleson measures with the $\d$-equation in a slightly more abstract framework than usual. We also consider a more recent result of Peter Jones which shows the existence of a solution of the $\d$-equation, which satisfies simultaneously a good $L_ı$ estimate and a good $L_1$ estimate. This appears as a special case of our main result which can be stated as follows: Let $(Ω,\cal{A},μ)$ be any measure space. Consider a bounded operator $u:H^1\ra L_1(μ)$. Assume that on one hand $u$ …

On Multivariate Matsaev's Conjecture

In this article, we study multivariate generalizations of the Matsaev's conjecture in commutative and non-commutative $L^p$-spaces.We prove that the multivariate analogue of Matsaev's conjecture is eventually false for all $1<p<\infty.$ We exhibit various joint dilation results on non-commutative $L^p$-spaces.

Holomorphic Functions of Exponential Type and Duality for Stein Groups with Algebraic Connected Component of Identity

We suggest a generalization of Pontryagin duality from the category of commutative Stein groups to the category of (not necessarily commutative) Stein groups with algebraic connected component of identity. In contrast to the other similar generalizations, in our approach the enveloping category consists of Hopf algebras (in a proper symmetrical monoidal category).