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1.
球面Hardy空间上Riesz平均的逼近   总被引:1,自引:0,他引:1  
引进了球面Hrady空间上Riesz平均算子及Peetre K模。讨论了Riesz平均算子在Hardy空间上的逼近性质。证明了Riesz平均算子与Peetre K模的强渐近等价关系。所得结果表明Peetre K模完全刻划了Riesz平均的逼近。  相似文献   

2.
在De Morgan代数上引入广义R0算子,举例说明了一般De Morgan代数中的广义R0算子不能构成t-模。引入强De Morgan代数的概念,讨论它的基本性质,证明强De Morgan代数L上的广义R0算子构成t-模(称为广义R0t-模)。给出若干重要反例,并证明强De Morgan代数上的广义R0t-模是左连续的。  相似文献   

3.
针对具有Caputo导数的二维时间分数阶扩散方程进行高精度有限元分析.首先,基于双线性元和L1逼近建立了一个全离散格式,并证明其在H~1模意义下的无条件稳定性;其次,借助Riesz投影和分数阶导数的技巧得到了L~2模意义下的最优误差估计,结合该元插值算子与Riesz投影算子之间的高精度结果和插值后处理技术,导出了H~1意义下的超逼近性质和超收敛结果.该结果是单独利用双线性插值算子和Riesz投影算子均无法得到的.最后,利用数值算例验证了理论分析的正确性.  相似文献   

4.
该文在圆盘代数A(D)中引入了一个数乘变换, 找到了多项式有界算子的多项式演算与Riesz函数演算之间的联系, 得到了Banach空间X上的一般多项式有界算子的泛函表示定理.  相似文献   

5.
李落清 《数学学报》1993,36(5):627-632
本文给出了研究乘子算子在全测度集上逼近的一种框架.在 Riesz 极大算子有界的条件下,确定了一类乘子算子在 Riesz 位势空间上几乎处处逼近的阶.并用于讨论广义 Bochner-Riesz 平均和 Abel-Cartwright 平均的点态逼近.  相似文献   

6.
设G是实数加群,B表示G上的无Order齐次Banach代数,表示B中的右平移可积算子全体.在一些合宜条件下,我们得到如下结果:(1)在中的算子关于F.Riesz和M.Riesz第一定理成立。(2)在中解析算子关于F.Riesz和M.Riesz第二定理成立。  相似文献   

7.
Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.扭Heisenberg-Virasoro代数是次数不超过1的微分算子代数的中心扩张,它是一类重要的无限维李代数,与一些曲线的模空间有关.文章主要研究扭Heisenberg-Virasoro代数上Hom-李代数结构,确定了扭Heisenberg-Virasoro代数上存在非平凡的Hom-李代数结构.  相似文献   

8.
引言.Dieudonne在[1](p.323问题5))中给出了复Banach空间Riesz算子的定义及充要条件。这个定义比笼统地称使Fredholm定理成立的算子为Riesz算子要具体,因而,也更有趣。显然这个定义是Dieudonne在深入地整理了Riesz紧算子理论之后而得到的。本文分两节:§1叙述Riesz算子的定义,比[1]约略简化,证明了二者同值;§2根据Riesz算子的定义导出了它的一些性质,说明对于Riesz算子,Fredholm定理依然成立。并且作为特例,包括了[2](p.430末两行)的命题。  相似文献   

9.
从微分算子角度理解核函数空间,借助经典Fourier变换研究核函数逼近问题.应用Fourier乘子算子和算子半群定义了一种光滑模,证明其与一种基于微分算子的K-泛函的等价性,由此给出了刻画核函数逼近收敛性的Jackson不等式.进一步证明,如果微分算子为Riesz势算子或Bessel势算子,逼近的收敛性可以转化为卷积算子逼近.特别地,给出了再生核Hilbert空间逼近的一种上界估计.  相似文献   

10.
赵晓晓  高寿兰  刘东 《数学学报》2016,59(6):775-782
Poisson代数是指同时具有代数结构和李代数结构的一类代数,其乘法与李代数乘法满足Leibniz法则.扭Heisenberg-Virasoro代数是一类重要的无限维李代数,是次数不超过1的微分算子李代数W(0)的普遍中心扩张,与曲线的模空间有密切联系.本文主要研究扭Heisenberg-Virasoro代数上的Poisson结构,首先确定了李代数W(0)上的Poisson结构,进而给出了扭Heisenberg-Virasoro代数上的Poisson结构.  相似文献   

11.
本文给出了一些用一族具有Riesz分解性质的效应代数黏合成齐次的效应代数的条件,并研究了通过线性MV-代数替换正交代数中的原子得到只含有1型原子的有限的齐次效应代数的方法。  相似文献   

12.
In this paper we introduce whales in the collection of subsets of the Boolean algebra of bands in a Dedekind complete Riesz space and employ them to give a short (and constructive) proof of the existence of universal completions for Archimedean Riesz spaces.

  相似文献   


13.
We describe all two dimensional unital Riesz algebras and study representations of them in Riesz algebras of regular operators. Although our results are not complete, we do demonstrate that very varied behaviour can occur even though all these algebras can be given a Banach lattice algebra norm.  相似文献   

14.
We consider the Multiplicative Decomposition Property (the multiplicative analogue of the Riesz Decomposition Property) for entry-wise ordered matrix algebras over the reals. We characterize for which matrix pairs such a decomposition exists and use this result to present necessary and sufficient conditions for a matrix algebra to enjoy the decomposition property by all its positive matrix pairs. Thus we describe all matrix algebras with the decomposition property.  相似文献   

15.
It is shown that an arbitrary interval of a pseudo-effect algebra is a pseudo-effect algebra and some results concerning Riesz decomposition properties, compatibilities and states are proved.  相似文献   

16.
We show that quotients of generalized effect algebras by Riesz ideals preserve some important special properties, e.g., homogeneity and hereditary Riesz decomposition properties; moreover, quotients of generalized orthoalgebras, weak generalized orthomodular posets, generalized orthomodular lattices and generalized MV-algebras with respect to Riesz ideals belong to the same class. We give a necessary and sufficient condition under which a Riesz ideal I of a generalized effect algebra P is a Riesz ideal also in the unitization E of P. We also study relations between Riesz ideals and central elements in GEAs and in their unitizations. In the last section, we demonstrate the notion of Riesz ideals by some illustrative examples. Received June 28, 2005; accepted in final form January 23, 2007.  相似文献   

17.
It is shown that to a classical Riesz product one can naturally assign a random walk; the spectrum of the shifts on the tail algebra of the random walk is defined by the measure to which the Riesz product converges. This observation is extended to general groups, which leads to some operator analogs of Riesz products. The properties of operator Riesz products are investigated.  相似文献   

18.
The paper consists of two parts. In the first part, we prove a noncommutative analog of the Riesz(— Markov—Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space. In the second part, using this result, we prove a weak version of a Burnside type theorem on twisted conjugacy for arbitrary discrete groups.  相似文献   

19.
We show that the quotient of a dimension effect algebra by its dimension equivalence relation is a unital bounded lattice-ordered positive partial abelian monoid that satisfies a version of the Riesz decomposition property. For a dimension effect algebra of finite type, the quotient is a centrally orthocomplete Stone–Heyting MV-effect algebra; moreover, an orthocomplete effect algebra in which equality is a dimension equivalence relation is the same thing as a complete Stone–Heyting MV-effect algebra.  相似文献   

20.
Let B be a unital commutative semi-simple Banach algebra. We study endomorphisms of B which are also quasicompact operators or Riesz operators. Clearly compact and power compact endomorphisms are Riesz and hence quasicompact. Several general theorems about quasicompact endomorphisms are proved, and these results are then applied to the question of when quasicompact or Riesz endomorphisms of certain algebras are necessarily power compact.  相似文献   

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