关于B-凸空间及其上黎斯算子West分解

给出 Ｂａｎａｃｈ空间列｛Ｘｉ｝ｉ＝１∞的 ｌｐ乘积Ｂ－凸的特征刻划, 证明Ｂ－凸空间上的每个黎斯算子可Ｗｅｓｔ分解,即分解成一个紧算子和一个拟幂 零算子的和．     

On the Decomposition of the Riesz Operator and the Expansion of the Riesz Semigroup

For a Riesz operator T on a reflexive Banach space X with nonzero eigenvalues denote by E(λ_i; T) the eigen-projection corresponding to an eigenvalue λ_i. In this paper we will show that if the operator sequence is uniformly bounded, then the Riesz operator T can be decomposed into the sum of two operators T_p and T_r: T = T_p + T_r, where T_p is the weak limit of T_n and T_r is quasi-nilpotent. The result is used to obtain an expansion of a Riesz semigroup T(t) for t ≥ τ. As an application, we consider the solution of transport equation on a bounded convex body.     

拟-*-A类算子的Riesz幂等元

证明了若T是拟-*-A类算子且λ_0是σ(T)的孤立点谱,则E是自共轭算子且满足EH=Ker(T-λ_0)=Ker(T-λ_0)~*,其中E是算子T关于λ_0的Riesz幂等元.     

g-上鞅的Riesz分解定理

本文给出了当终端时间趋于无穷时一类有限时间区间上的倒向随机微分方程的解的收敛性,并且证明了这类解平方收敛到特定的无穷时间区间上的倒向随机微分方程的解.本文主要研究了由倒向随机微分方程生成的非线性期望及其鞅的性质,证明了当生成元g是超线性时的g-上鞅Riesz分解定理.并且指出经典鞅论中的Riesz分解定理和下期望(又称最小期望)对应的上鞅Riesz分解定理是g-上鞅Riesz分解定理的两种特殊情况.     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

Riesz Idempotent and Algebraically M-hyponormal Operators

Let T be an M-hyponormal operator acting on infinite dimensional separable Hilbert space and let be the Riesz idempotent for λ₀, where D is a closed disk of center λ₀ which contains no other points of σ (T). In this note we show that E is self-adjoint and As an application, if T is an algebraically M-hyponormal operator then we prove : (i) Weyl’s theorem holds for f(T) for every (ii) a-Browder’s theorem holds for f(S) for every and f ∈ H(σ(S)); (iii) the the spectral mapping theorem holds for the Weyl spectrum of T and for the essential approximate point spectrum of T.     

关于集值下鞅Riesz分解的注记

在X*可分的条件下给出了集值序列及集值下鞅的一些结果,在此基础上,利用支撑函数,给出了Banach空间集值下鞅的Riesz分解定理。     

弱集值Amart的Riesz分解

本文证明了弱集值Amart可Riesz分解的充要条件。     

Riesz Potentials and Liouville Operators on Fractals

An analogue to the theory of Riesz potentials and Liouville operators in R ⁿ for arbitrary fractal d-sets is developed. Corresponding function spaces agree with traces of Euclidean Besov spaces on fractals. By means of associated quadratic forms we construct strongly continuous semigroups with Liouville operators as infinitesimal generator. The case of Dirichlet forms is discussed separately. As an example of related pseudodifferential equations the fractional heat-type equation is solved.     

Disjointness Preserving Operators on Complex Riesz Spaces

It is proven that ifE and F are complex Riesz spaces and ifT is an order bounded disjointness preserving operator fromE intoF , then This fundamental result of M. Meyer is obtained by elementary means using as the main tool the functional calculus derived from the Freudenthal spectral theorem. It is also shown that ifT is an order bounded disjointness preserving operator, a formula of the form holds. It implies a polar decomposition of an order bounded disjointness preserving operator as the product of a Riesz homomorphism and an orthomorphism. Results of P. Meyer-Nieberg in this regard are generalized.     

齐次群上的限制算子与Riesz平均

主要讨论一类齐次群上限制算子的映照性质,并且应用所得结果证明这类齐次群上Riesz平均的混合范数有界性。     

S-harmonic Function and RieszDecomposition Theorem of Superprocesses

RecentlyItheremanyprogressinthetheoryofsuperprocesses(seeLZ'4--gi).Inthispaper,wewillestablishtheRicszdecompositiontheoremofexcessivefunctionsofaclassofsuperprocesses,andgeneralizetheclassicalRicszdecompositiontheoremofHuntprocess.FortheconstructionofsupcrprocesscswecanseeL2,4,sj.ConsiderthefollowingrealfunctionPX,9(x,z)=a(x)z b(x)zZ J,(e":--I "z)n.(du),(1)Pcowheren.(du)isakernelfromR'lto(0,~)and'a(x),b(x)andA(x)~I(uZAu)n.(du)areJ0positiveboundedBorclfunctions.AssumingthatE~{Et,11.}is…     

Perturbation Stability of Coherent Riesz Systems under Convolution Operators

We study the orthogonal perturbation of various coherent function systems (Gabor systems, Wilson bases, and wavelets) under convolution operators. This problem is of key relevance in the design of modulation signal sets for digital communication over time-invariant channels. Upper and lower bounds on the orthogonal perturbation are formulated in terms of spectral spread and temporal support of the prototype, and by the approximate design of worst-case convolution kernels. Among the considered bases, the Weyl–Heisenberg structure which generates Gabor systems turns out to be optimal whenever the class of convolution operators satisfies typical practical constraints.     

On the Polar Decomposition of the Product of Two Operators and Its Applications

Let T = U|T| and S = V|S| be the polar decompositions. In this paper, we shall obtain the polar decomposition of TS as TS = UWV|TS|, where |T||S^*| = W||T||S^*|| is the polar decomposition. Next, we shall show that TS = UV|TS| is the polar decomposition if and only if |T| commutes with |S^*|. Lastly, we shall apply this result to binormal and centered operators. We shall obtain characterizations of these operator classes from the viewpoint of the polar decomposition.