Automatic continuity of transversal distributions
Jure Kališnik
本文证明了横向分布具有自动连续性。
我们证明了每一个横向分布都是自动连续的。
We prove that every transversal distribution is automatically continuous.
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On automatic continuity of operators from ordered to topological vector spaces
本文研究了从有序到拓扑向量空间的算子连续性和有界性，探讨了Frechet空间到拓扑向量空间的算子自动连续性，特别研究了Levi和Lebesgue算子。
Automatic continuity of biseparating maps
证明了向量值连续函数空间之间的双分离映射通常是自动连续的。然而，我们也讨论它不为真的特殊情况。
In this article we shall focus on the derivations on module extension of Banach algebras and determine the general structure of them. Then we obtain some results concerning the automatic continuity of these mappings.
On some automatic continuity theorems
利用乘性线性泛函给出了单位一致拓扑代数和饱和局部乘法凸代数的刻画。本文将一致完备拓扑代数中的一些自动连续性定理推广到更大的代数类中。结果和应用。
On a conjecture concerning some automatic continuity theorems
设A和B是具有单位元的交换局部凸代数。假设A是一致拓扑代数。设h是A到B的单同态。在附加的假设下，我们通过Im（h）的闭包的根（或强根）与Im（h）只有零点作为公共点，刻画了同态h^（-1）/ Im（h）的连续性.这就回答了关于一致拓扑代数上自动连续性定理的一个猜想。
Automatic continuity and weighted composition operators between spaces of vector-valued differentiable functions
证明了向量值可微函数空间之间的线性双分离映射是加权复合映射。因此，这样的映射总是连续的。
Let $\mathcal{A}$ and $\mathcal{U}$ be Banach algebras and $θ$ be a nonzero character on $\mathcal{A}$. Then the \textit{Lau product Banach algebra} $\mathcal{A}\times_θ\mathcal{U}$ associated with the Banach algebras $\mathcal{A}$ and $\mathcal{U}$ is the $l^1$-direct sum $\mathcal{A}\oplus\mathcal{U}$ equipped with the algebra multiplication $(a,u)(a',u')=(ab,θ(a)u'+θ(a')u+uu')\, (a,a'\in\mathcal{A},u,u'\in\mathcal{U})$ and $l^1$-norm. In this paper we shall investigate the derivations and multipliers from this Banach algebras and study the automatic continuity of these mappings. We also stu…
Automatic continuity for the unitary group
证明了从无限维酉群或正交群到可分群的同态是连续的。
Automatic norm continuity of weak* homeomorphisms
证明了在某类不可分巴拿赫空间E中，对偶球的范数拓扑可用其弱 * 拓扑定义.因此，E中空间的两个球之间的任何弱 * 同胚自动是范数连续的。
Automatic continuity of biorthogonality preservers between compact C$^*$-algebras and von Neumann algebras
该研究证明了对偶/紧C$^*$-代数及冯·诺依曼代数间的保双正交线性满射具有自动连续性，推进了算子代数映射性质研究。
It is well known that weakly continuous semigroups defined over $\mathbb{R}_{+}$ are automatically strongly continuous. We extend this result to more generally defined semigroups, including multiparameter semigroups.
Automatic Continuity of $σ$-Derivations on $C^*$-Algebras
设$A$是作用在Hilbert空间$H$上的$C^*$ -代数，$σ:A\to B(H)$是线性映射，$d:A\to B(H)$是$σ$ -导子.推广Sakai的著名定理，证明了如果$σ$是连续的$*$ -映射，则$d$是自动连续的.另外，证明了如果$d$是一个连续的$*-σ$ -导子，则存在一个连续的线性映射$Σ:A\to B(H)$，使得$d$是$*-Σ$ -导子.本文还讨论了所谓的$*-(σ,τ)$ -导子的连续性。
On Automatic Continuity of 3-Homomorphisms on Banach Algebras
（Banach）代数之间的线性映射$ϕ:{\mathcal A}\to {\mathcal B} $称为3-同态，如果对每个$a, b, c \in {\mathcal A}$都有$ϕ(abc)=ϕ(a)ϕ(b)ϕ(c)$.研究了巴拿赫代数上具有有界逼近恒等式的3-同态，并从两个方面证明了$C^*$ -代数之间的每一个保对合同态都是模减的.
Automatic continuity of new generalized derivations
本文研究 Banach 代数与 C*-代数上 n 阶强广义导子的自动连续性，通过定义此类导子并探讨其性质，为算子代数理论提供新结果。
In 1952, Michael posed a question about the functional continuity of commutative Frechet algebras in his memoir, known as Michael problem in the literature. We settle this in the affirmative along with its various equivalent forms, even for the non-commutative case. Indeed, we continue our recent works, and develop two approaches to directly attack these problems. The first approach is to show that the test case for this problem, the Frechet algebra of all entire functions on the Banach space of all bounded complex sequences, is, in fact, a Frechet algebra of all complex formal power series in…
Automatic continuity of biorthogonality preservers between weakly compact JB$^*$-triples and atomic JBW$^*$-triples
该研究证明了不含无限维秩一直和项的弱紧JB$^*$-三元组到另一JB$^*$-三元组、以及同类原子JBW$^*$-三元组之间的双正交保持线性满射均自动连续，并由此得到不含秩一直和项的原子JBW$^*$-三元组同构的等价条件。
Harmonic analysis and automatic continuity in the context of generalized differential subalgebras
本文引入并系统研究$(k,p,q)$-微分子代数类，证明其具有函数演算封闭性、$^*$-正则性、Wiener性质及自动连续性等关键性质。
A note on finite-dimensional quotients and the problem of automatic continuity for twisted convolution algebras
本文证明扭曲卷积代数的有限余维闭理想商为半单代数，并借此扩展自动连续性结果，构造大量相关例子。
Automatic time continuity of positive matrix and operator semigroups
本文研究无可测性假设的正矩阵半群，证明其在原点附近有界时自动连续，并将结果推广到序列空间上的正算子半群。
We prove that all the composition operators $T_f(g):= f\circ g$, which take the Adams-Frazier space $W^{m}_{p}\cap \dot{W}^{1}_{mp}(\mathbb{R}^n)$ to itself, are continuous mappings from $W^{m}_{p}\cap \dot{W}^{1}_{mp}(\mathbb{R}^n)$ to itself, for every integer $m\geq 2$ and every real number $1\leq p<+\infty$. The same automatic continuity property holds for Sobolev spaces $W^m_p(\mathbb{R}^n)$ for $m\geq 2$ and $1\leq p<+\infty$.
We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its commutant $M'$ and acting as the $*$-operation on the centre. We also prove a generalized version of the BT-Theorem which enables us to see that such an intertwiner must be necessarily bounded. It is shown that this extension of the BT-Theorem leads to the automatic boundedness of quite general operators which intertwine the identity map of a von Neumann algebr…
We study the question how quickly products of a fixed conjugacy class in the projective unitary group of a II${}_1$-factor von Neumann algebra cover the entire group. Our result is that the number of factors that are needed is essentially as small as permitted by the $1$-norm - in analogy to a result of Liebeck-Shalev for non-abelian finite simple groups. As an application of the techniques, we prove that every homomorphism from the projective unitary group of a II${}_1$-factor to a polish SIN group is continuous. Moreover, we show that the projective unitary group of a II${}_1$-factor carries…
Continuity and Equicontinuity of Transition Semigroups
本文研究赋范对偶对上的半群关于用对偶定义的拓扑的连续性和等度连续性。特别是，我们解决的问题是否连续的半群已经意味着（本地/准）等度连续。我们应用我们的结果转移半群，并表明，适当的假设下，$E$，每一个过渡半群在$C_b(E)$是连续的严格拓扑$β_0$是自动拟等度连续的。给出了$C_b(E)$上$β_0$ -连续半群的几个刻画，并给出了巴拿赫空间值马尔可夫过程的转移半群是$β_0$ -连续的一个便利条件.
We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors ([Bull. Lond. Math. Soc. 53 (2021)]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyo…
Automatic continuity and $C_0(Ω)$-linearity of linear maps between $C_0(Ω)$-modules
设$Ω$是局部紧Hausdorff空间。证明了Banach $C_0(Ω)$ -模之间的任何局部$\mathbb{C}$ -线性映射（其中“局部”是比$C_0(Ω)$ -线性更弱的概念）是“近$C_0(Ω)$ -线性”和“近有界”的.作为一个应用，Hilbert $C_0(Ω)$ -模之间的局部$\mathbb{C}$ -线性映射$θ$自动地是$C_0(Ω)$ -线性的.此外，如果$Ω$不包含孤立点，则Hilbert $C_0(Ω)$ -模之间的任何$C_0(Ω)$ -线性映射是自动有界的。另一个应用是，如果两个Banach空间之间的映射序列$\{θ_n\}$“保持$c_0$ -序列”（或“保持超$c_0$ -序列”），则对于足够大的$n$，$θ_n$是有界的，并且它们有一个公共界。此外，我们还证明了如果$θ$是从“完全”本质Banach $C_0(Ω)$ -模$E$到“完全”Hilbert $C_0(Δ)$ -模$F$的双射“双分离”线性映射（其中$Δ$是另一个局部紧Hausdorff空间），则$θ$是“近有界的”（事实上，如果$Δ$或$Ω$不包含孤立点，则它是自动有界的），并且存在同胚$σ: Δ\rightarrow Ω$使得$θ(e\cdot φ) = θ(e)\cdot φ\circ σ$（$e\in E, φ\in C_0(Ω)$）.
Starting from Sinclair's 1976 work {\it Automatic Continuity of Linear Operators}, Cambridge University Press, (1976), on automatic continuity of linear operators on Banach spaces, we prove that sequences of intertwining continuous linear maps are eventually constant with respect to the separating space of a fixed linear map. Our proof uses a gliding hump argument. We also consider aspects of continuity of linear functions between locally convex spaces and prove that such that a linear function $T$ from the locally convex space $X$ to the locally convex space $Y$ is continuous whenever the sep…
Let A and U be Banach algebras such that U is also a Banach A- bimodule with compatible algebra operations, module actions and norm. By defining an approprite action, we turn l1-direct product A item U into a Banach algebra such that A is closed subalgebra and U is a closed ideal of it. This algebra, is in fact semidirect product of A and U which we denote it by A litem U and every semidirect products of Banach algebras can be represented as this form. In this paper we consider the Banach algebra A litem U as mentioned and study the derivations on it. In fact we consider the automatic continui…
Automatic continuity of operator semigroups in the Calkin algebra
本文研究Calkin代数中的算子半群，利用BDF理论将正规$C_0$-半群与扩张关联，并证明在自然情形下，强算子拓扑连续性蕴含均匀连续性。
Achievement of continuity of $(ϕ,ψ)$-derivations without continuity
设$\calak$是作用在Hilbert空间$\calhk$上的$C^*$ -代数，并且$ϕ, ψ$是从$\calak$到$B(\calhk)$的映射，它们不一定是线性或连续的.一个$(ϕ, ψ)$ -推导是一个线性映射$d: \calak \to B(\calhk)$，使$$d(ab)=ϕ(a)d(b)+d(a)ψ(b)\quad (a,b\in \calak).$$我们证明，如果$ϕ$是一个乘法（不一定是线性）$*$ -映射，那么每个$*$ - $(ϕ,ϕ)$ -推导是自动连续的。利用这一事实，我们证明了每个从$\calak$到$B(\calhk)$的$*$ - $(ϕ,ψ)$ -导子$d$是连续的当且仅当$*$ -映射$ϕ$和$ψ$分别是左和右$d$ -连续的.
A General Framework for Operator Continuity between Riesz Spaces
本文提出一个统一框架，研究Riesz空间间基于广义序收敛的$\mathcal{FG}$-序连续算子，证明其有序有界性、模保持性、序连续性与带刻画，并给出正算子的扩张定理。
We give a survey of Husain, Ng and Liang's results concerning the automatic continuity of algebra homomorphisms. We also give the improvements obtained by Joseph, Akkar, Oudadess, Zelazko and ourselves.
Local triple derivations on C*-algebras and JB*-triples
在第一个结果中，我们证明了JB $^*$ -三元组上的每一个连续的局部三元组导子都是三元组导子。我们还给出了一个自动连续性的结果，即我们证明了JB $^*$ -三元组上的局部三元组导子是连续的，即使事先没有假设是这样的。特别地，C $^*$ -代数上的每一个局部三元导子都是三元导子.我们还探讨了C $^*$ -代数上的（有界局部）三重导子和广义（Jordan）导子之间的联系。
Characterisation of the Berkovich Spectrum of the Banach Algebra of Bounded Continuous Functions
对完备赋值域k和拓扑空间X，证明了X上有界连续k值函数的Banach k-代数Cbd（X，k）的Berkovich谱的基础拓扑空间的普适性.这一结果产生了三个应用：局部域上自动连续性问题的Kaplansky猜想的模拟的部分解，Cbd（X，k）的两个基域扩展的比较，以及非阿基米德Gel'fand理论.
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