S. Kutateladze
An order bounded functional on a Riesz space is a difference of Riesz homomorphisms if and only if the kernel of this functional is a Riesz subspace of the ambient Riesz space.
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In this paper, we study the connextion between lattice and Riesz homomorphisms in Riesz spaces. We prove, under a certain condition, that any lattice homomorphism on Riesz space is a Riesz homomorphism. This fits in the type of results by Mena and Roth [7], thanh [9], Lochan and Strauss [5] and Ercan and Wickstead [2].
Truncation bands, unitality, and homomorphisms in truncated Riesz spaces: Boulabiar's problems and beyond
本文解答Boulabiar关于截断Riesz空间的三个问题：截断带投影等价于主投影，单位性由不动点上确界刻画，并给出截断同态非Riesz同态的反例及其模无穷小的修正。
Let $L$ be a Riesz space with a strong unit $e>0$.$\mathfrak{\ }$We show that a unital linear functional $H:L\rightarrow \mathbb{R}$ satisfies $% H\left( u\right) \neq 0$ for any strong unit $u\in L$ if and only if $H$ acts like a Riesz homomorphism on every $e$-clean vector subspace of $L.$ We deduce that $L$ is $e$-clean if and only if any unital linear functional $% H:L\rightarrow \mathbb{R}$ such that $H\left( u\right) \neq 0$ for any strong unit $u\in L$ is a Riesz homomorphism.
Riesz* Homomorphisms on the copositive Cone
本文针对余正优化领域中保余正线性映射刻画的问题，提出仅用序理论论证的新方法，得到Riesz*同态的表示定理，统一了相关成果并修正了标准线性映射保余正性的刻画。
The modulus of an order bounded functional on a Riesz space is the sum of a pair of Riesz homomorphisms if and only if the kernel of this functional is a Grothendieck subspace of the ambient Riesz space. An operator version of this fact is given.
Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More precisely, we use of a version of the remarkable Riesz-Kantorovich formulae and Fatou property for bounded order bounded homomorphisms to allocate the desired structures. Moreover, we show that unbounded convergence on a locally solid lattice group is topological and we investigate some applications of it. Also, some necessary and sufficient conditions for compl…
The main objective of this article is to introduce Euler-Riesz difference sequence spaces of fractional order $τ $ along with infinite matrices. Some topological properties of these spaces are considered here along with the Schauder basis, $α -,β-$ and $γ-$duals of the spaces. Keywords: Euler-Riesz difference sequence space, difference operator $\left(Δ^τ \right)$, Schauder basis, infinite matrices and $α -,β-$ and $γ-$duals .
In this note we prove Yosida duality --- that is: the category of compact Hausdorff spaces with continuous maps is dually equivalent to the category of uniformly complete Archimedean Riesz spaces with distinguished units and unit-preserving Riesz homomorphisms between them.
Linear combinations of exponentials $e^{iλ_kt}$ in the case where the distance between some points $λ_k$ tends to zero are studied. D. Ullrich has proved the basis property of the divided differences of exponentials in the case when the groups consist of equal number of points all of them are close enough to integers. We have generalized this result for groups with arbitrary number of close points and obtained a full description of Riesz bases of exponential divided differences. The application to a control problem is presented.
Let $E$ be a Riesz space and let $E^{\sim}$ denote its order dual. The orthomorphisms $Orth(E)$ on $E,$ and the ideal center $Z(E)$ of $E,$ are naturally embedded in $Orth(E^{\sim})$ and $Z(E^{\sim})$ respectively. We construct two unital algebra and order continuous Riesz homomorphisms \[ γ:((Orth(E))^{\sim})_{n}^{\sim}\rightarrow Orth(E^{\sim})\text{ }% \] and \[ m:Z(E)^{\prime\prime}\rightarrow Z(E^{\sim}) \] that extend the above mentioned natural inclusions respectively. Then, the range of $γ$ is an order ideal in $Orth(E^{\sim})$ if and only if $m$ is surjective. Furthermore, $m$ is surj…
We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear. And we prove a polynomial version of the Kantorovich extension theorem.
Let $E$ be a Banach lattice. Its ideal center $Z(E)$ is embedded naturally in the ideal center $Z(E')$ of its dual. The embedding may be extended to a contractive algebra and lattice homomorphism of $Z(E)"$ into $Z(E')$. We show that the extension is onto $Z(E')$ if and only if $E$ has a topologically full center. (That is, for each $x\in E$, the closure of $Z(E)x$ is the closed ideal generated by $x$.) The result can be generalized to the ideal center of the order dual of an Archimedean Riesz space and in a modified form to the orthomorphisms on the order dual of an Archimedean Riesz space.
Frames containing a Riesz basis and preservation of this property under perturbation
Aldroubi已经示出了如何可以使用$l^2(N)$上的有界算子$U$从一个帧$\ftu $开始构造任何帧$\gtu$。利用$U$的性质研究了框架的过完备性.我们还讨论了扰动的框架的意义上说，两个框架是"关闭“，如果某个操作是紧凑的。这样我们得到了一个等价关系，它具有同一个等价类的成员具有相同的超完备性的性质。另一方面，我们表明，在Paley-Wiener意义上的扰动不具有此属性。最后，我们构造了一个下模有界但不含Riesz基的框架，这个构造是基于框架表示的无条件收敛与框架元素中的收敛级数不需要无条件收敛之间的微妙区别。
Divergence Phase Index: A Riesz-Transform Framework for Multidimensional Phase Difference Analysis
本研究提出基于Riesz变换的散度相位指数DPI，将经典希尔伯特变换相位度量拓展至高维，在多类数据集验证了其在信号与图像相位变化检测中的有效性，可应用于多个相关领域。
Let $X$ be a complex Banach space. The connection between algebra homomorphisms defined on subalgebras of the Banach algebra $\ell^{1}(\mathbb{N}_0)$ and the algebraic structure of Cesàro sums of a linear operator $T\in \mathcal{B}(X)$ is established. In particular, we show that every $(C, α)$-bounded operator $T$ induces - and is in fact characterized - by such an algebra homomorphism. Our method is based on some sequence kernels, Weyl fractional difference calculus and convolution Banach algebras that are introduced and deeply examined. To illustrate our results, improvements to bounds for A…
Adjoints, Order and Spectral Moduli on $L^2(T)$
本文研究条件空间 $L^2(T)$ 上 $T$-强有界算子的伴随与序结构，定义并比较里斯-坎托罗维奇序模和谱模，证明 $T$-正则算子构成戴德金完备序理想，伴随为序自同构。
Riesz-means bounds for functional-difference operators for mirror curves
本文针对镜面曲线相关的泛函差分算子 H(ζ)，在 λ 趋于无穷时给出其 Riesz 平均的估计，方法基于 Laptev-Schimmer-Takhtajan 的谱分析框架。
Weyl asymptotics for functional difference operators with power to quadratic exponential potential
该研究延续相关计划，改进既有技术，针对带幂到二次指数势的泛函差分算子，提出研究其谱渐近性的新方法，涵盖特定文献中的势，通过扩张高斯方差完成证明。
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