Fp空间上相关的复合算子

本文研究了F_p空间上的复合算子的几个问题.应用泛函分析的方法研究了F_p(相应地,F_p,0)空间到Bloch空间的复合算子的有界性和紧性的若干充分和必要条件.此外,也刻画了当1 ≤ p < ∞时从Bloch空间到F_p空间的等距复合算子并且证明了当0 < p < ∞时F_p,0上的复合算子不具有Fredholm性.     

POWERS OF OPERATORS DOMINATED BY STRICTLY SINGULAR OPERATORS

It is proved that every positive operator R on a Banach latticeE dominated by a strictly singular operator T:E E satisfiesthat the R⁴ is strictly singular. Moreover, if E is order continuousthen the R² is already strictly singular.     

算子空间中秩一算子的稠密性

设u是Hilbert空间上的σ-弱闭算子空间,称u具有性质（P）,如果u中秩－算子生成的子空间在u中是σ－弱稠密的,称u具有扩张性质（P）,如果u以及包含u的每个σ－弱闭子空间都具有性质（P）,本文研究了性质（P）和扩张性质（P）,给出了它们的等从描述。     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,δ的有界性和紧性以及加权复合算子Tφ,δ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,φ的有界性问题.主要得到以下结论: (i)Tφ,δ是空间βp到βq的有界算子之充要条件; (ii)T1,φ是空间βp到βq的紧算子之充要条件; (iii)T1,φ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

p-Bloch空间上的复合算子和加权复合算子

本文系统地讨论了单位圆中p-Bloch空间上复合算子T1,ψ的有界性和紧性以及加权复合算子Tψ,ψ的有界性,同时也在小p-Bloch空间上讨论了复合算子T1,ψ的有界性问题.主要得到以下结论(i)Tψ,ψ是空间βp到βq的有界算子之充要条件;(ii)T1,ψ是空间βp到βq的紧算子之充要条件;(iii)T1,ψ是空间βp0到βq0的有界算子之充要条件等.从空间或算子上扩展了文[1,4]的相应结论.     

A—光滑正则化算子

本文研究了紧算子方程的Moore-Penrose广义解的逼近,引进了A-导数的概念和对应的A-光滑正则化算子.这个双参数的A-光滑正则化算子族有明显的变分意义,并且包含正则化算子作为它的特殊情形,以(修正的)截断奇异值分解方法作为它的极限情形.这些正则化算子的性质表明它们有广阔的实际应用可能性.     

L~p ESTIMATES FOR BI-INVARIANT OPERATORS ON CLASSICAL GROUPS

§1.ＩｎｔｒｏｄｕｃｔｉｏｎＳｕｐｐｏｓｅｔｈａｔＧｉｓａｃｏｍｐａｃｔＬｉｅｇｒｏｕｐａｎｄ^ＧｉｓａｍａｘｉｍａｌｃｏｌｌｅｃｔｉｏｎｏｆｉｎｅｑｕｉｖａｌｅｎｔｉｒｒｅｄｕｃｉｂｌｅｕｎｉｔａｒｙｒｅｐｒｅｓｅｎｔａｔｉｏｎｏｆＧ.Ｇｉｖｅｎａｂｏｕｎｄｅｄｍｕｌｔｉｓｅｑｕｅｎｃｅ{ｍ(λ)}λ∈^Ｇ,ｍ(λ)∈Ｃ｜,ｄｅｆｉｎｅｔｈｅｏｐｅｒａｔｏｒＴｏｎｔｈｅｓｐａｃｅｏｆｆｉｎｉｔｅｌｉｎｅａｒｃｏｍｂｉｎａｔｉｏｎｓｏｆｅｎｔｒｙｆｕｎｃｔｉｏｎｓｏｎＧｂｙｗｒｉｔｉｎｇ(Ｔ^ｆ)(λ)=ｍ(λ)^…     

组合线性算子

本文给出一种构造组合线性逼近算子的方法，由此可得到具有特殊逼近性质的线性算子．     

POSITIVE COMPACT OPERATORS

Abstract

We present an overview of relatively recent progress in the theory of positive operators which finds its origins in the classical spectral theory of Perron-Frobenius for positive matrices.     

SINGULAR INTEGRAL OPERATORS ANDSINGULAR QUADRATURE OPERATORSASSOCIATED WITH SINGULAR INTEGRAL EQUATIONS

1IntroductionSingUlarlintegralequations(SIEs)withCauchytypekernelsoftheformappearfrequelltlyinproblemsOfthetheoriesofelasticity.Heretheinputfunctionsa)b,f,l,aretheH5lder-continuousfunctionsfortheirvariables,Aisagivenconstant,anditisrequiredtofindthesolutionWintheclassho[1,2].Theclassicaltheoryoftheseequationsisrathercomplete[1,2].Inthepasttwentyyearsagreatdealofinteresthasarisenintheirnumericalsolution.VariouscollocationmethodsforSIEshaveappeared,forwhichsomereferencescanbefoundinthesurv…     

STEKLOV－POINCARE算子与自然积分算子及GREEN函数间的关系

ＳＴＥＫＬＯＶ－ＰＯＩＮＣＡＲＥ算子与自然积分算子及ＧＲＥＥＮ函数间的关系余德浩（中国科学院计算数学与科学工程计算研究所）ＯＮＲＥＬＡＴＩＯＮＳＨＩＰＢＥＴＷＥＥＮＳＴＥＫＬＯＶ－ＰＯＩＮＣＡＲＥＯＰＥＲＡＴＯＲＳＡＮＤＮＡＴＵＲＡＬＩＮＴＥＧＲＡＬ...     

多重拉普拉斯运算的扩充

<正> 设 U(P)≡U(x,y)为一二元的可积函数,我们以μ(U;P;r)代表 U(x,y)在以 P 为中心,r 为半径的圆周上之平均值,而以 V(U;P;r)代表 U(x,y)在以P为中心,r 为半径的圆域内部的平均值,即     

关于拟-*-A(k)算子的注记

本文引入了拟-?-A(k)算子并研究其谱性质如下：(i)如果T 是拟?-A(k)算子,其中0相似文献   

ON COMPLETELY SPECTRAL OPERATORS

In this paper we first introduce the concept of completely spectral operators and discuss its various properties; next, we consider spectral synthesis for this kind of operators and partly generalize Wermer’s result [1] on spectral synthesis for completely normal operators; finally, we investigate the problem of unitary equivalence of resolutions of the identity for completely spectral operators. Let \[\mathcal{X}\] be a separable Hilbert space and \[\mathcal{B}(\mathcal{X})\] the algebra of all bounded linear operators on \[\mathcal{X}\]. Let Lat T denote the lattice of all invariant subspaces of \[T \in \mathcal{B}(\mathcal{X})\] Definition 1. An operator \[T \in \mathcal{B}(\mathcal{X})\] is completely spectral if T is spectral and reductive. Proposition 1. T is a completely spectral operator if and only if T* is a completely spectral operator. Proposition 2. If T is a completely spectral operator and \[\mathcal{U} \in \] Lat T, then the restriction of T to \[\mathcal{U}\] is a completely spectral operator. Proposition 3. Let T be a spectral operator. If any pair of complementary subspaces of T is invariant under T, then T is similar to a completely spectral operator. Proposition 4. If T is a completely spectral operator, then T = N+Q, where N is a normal operator and Q is a quasinilpotent operator commuting with N. Moreover, every \[\mathcal{U} \in \] LatT reduces both N and Q. Difinition 2. We say that spectral synthesis holds for T, provided that for any \[\mathcal{U} \in \]LatT, which is not {0}, the set of root vectors of T contained in \[\mathcal{U}\] is complete in \[\mathcal{U}\]. Theorem 1, Let T be a completely spectral operator and let the set pf. root vectors of T be complete in \[\mathcal{U}\]. Then the spectral synthesis holds for T. The following lemma generalizes Theorem 5 of Dunford's [2]. Lemma. Let\[{E_{\text{1}}}(\sigma ),{E_2}(\sigma )\] be resolutions of the identity for bounded spectral operators T1, T2 respectively, on Banach space \[\mathcal{U}\], and let A be a bounded linear operator on \[\mathcal{U}\],If AT1 = T2A, then \[A{E_{\text{1}}}(\sigma ) = {E_2}(\sigma )A\]. Theoerm 2. Let T1, T2 be completely spectral operators. Their resolutions of the identity are \[{E_{\text{1}}}(\sigma ),{E_2}(\sigma )\], respectively. If T1 is a quasi-affine transform of T2, then ,\[{E_{\text{1}}}(\sigma )\] and \[{E_2}(\sigma )\] are unitarily equivalent.     

算子的拟酉等价性

本文在复的，可析的、无限维Ｈｉｂｅｒｔ空间Ｈ中引进了算子拟酉等价性的概念；获得了几个重要结果。     

D<Mk>型算子及其豫解式

在本文中,我们引入四类D<M_k>型算子,并讨论了它们的若干性质.它们都是无界的且在一定意义下是可以分解的,但它们的预解式的增长级却可以较高,因此在应用中比较方便.     

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

Around the central theme of "square root" of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.