共查询到18条相似文献,搜索用时 109 毫秒
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设H1和H2是两个Hilbert空间, B(H1,H2)表示从H1到H2的所有有界线性算子的集合, T和S分别是H1和H2的两个闭子空间. 如果存在线性算子X ∈ B(H2,H1)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A(2)T,S. 该文进一步研究了线性算子广义逆A(2)T,S存在的若干等价条件及其性质,建立了算子广义逆A(2)T,S的表示形式. 相似文献
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刘锐 《数学物理学报(A辑)》2007,27(3):385-391
该文给出了单位球面间等距算子在非满情况下的一些性质, 以及在这种情况下算子值域空间的一些结构特征, 并由此得出从c0(Gamma)到l∞-空间单位球面之间非满等距算子能够延拓的充要条件. 相似文献
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讨论一类不可分解的∑e1型Banach空间上有界线性算子的谱的特殊性质;给出了∑e1型Banach空间上一致有界C0半群稳定性的一个谱特征,并给出稳定性定理的一个应用. 相似文献
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罗罗 《数学物理学报(A辑)》2007,27(2):204-207
作者研究了CN 中单位球B上不同Hardy空间之间的乘法算子, 给出了有界的乘法算子Mg: Hp(B) → Hq(B)$的特征. 相似文献
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该文利用修正的带权 K- 泛函K2σ f, t2)w,p, 考虑Gamma算子在Lp~ (1≤p ≤∞)空间带权同时逼近, 给出了它的 B -型强逆不等式. 相似文献
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该文引入了 cut*空间的概念,所谓的 cut*空间是指去掉任意一点连通,去掉任意两点不连通的连通空间.通过对其性质的讨论,得到如下主要结论: 首先得到cut*空间中每个点非开即闭,并且cut*空间中有无限多个闭点;其次讨论了一类特殊的 cut*空间,即去掉一点是COTS的 cut* 空间.指出``$X$是 cut*空间,任意 $x\inX,X\setminus\{x\}$是不可约cut空间'这样的空间类是不存在的.在文章的最后,讨论了去掉一点是LOTS的 cut*空间的覆盖性质,得到这样的空间是紧空间或Lindel\"of空间的结论. 相似文献
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首先给出赋范线性空间中的非空集合C的逼近紧性的等价描述. 如所周知, 如果C是Banach空间X中的一个逼近紧的半Chebyshev闭集, 那么由X到C的度量投影算子πc是连续的. 当X是中点局部一致凸的Banach 空间, 利用Banach空间几何的技巧证得: C的逼近紧性对投影算子πc的连续性也是必要的. 利用这个一般结论给出: 当T是由逼近紧且严格凸的Banach空间$X$到中点局部一致凸Banach空间Y的有界线性算子时, T有连续的Morse-Penrose度量广义逆T+$的充分必要条件. 相似文献
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Consider the Sobolev embedding operator from the space of functionsin W1,p(I) with average zero into Lp, where I is a finite intervaland p>1. This operator plays an important role in recentwork. The operator norm and its approximation numbers in closedform are calculated. The closed form of the norm and approximationnumbers of several similar Sobolev embedding operators on afinite interval have recently been found. It is proved in thepaper that most of these operator norms and approximation numberson a finite interval are the same. 相似文献
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Hypercyclic and Chaotic Convolution Operators 总被引:3,自引:0,他引:3
Every convolution operator on a space of ultradifferentiablefunctions of Beurling or Roumieu type and on the correspondingspace of ultradistributions is hypercyclic and chaotic whenit is not a multiple of the identity. The operator of differentiationis hypercyclic on the space A, but it need not be hypercyclicon radial weighted algebras of entire functions. 相似文献
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彭志刚 《数学物理学报(A辑)》2008,28(5):945-957
设 H 是一个Hilbert空间. B(H) 表示所有H 到 H 的有界线性算子构成的Banach空间. 设 T= {f(z): f(z)=zI-∑∞n=2 znAn 在单位圆盘|z|<1上解析, 其中系数An是 H 到 H 的紧正Hermitian算子, I 表示 H 上的恒等算子, ∑∞n=2 n(An x, x) ≤1 对所有x ∈H, ∣|x∣∣=1 成立. 该文研究了函数族 T 的极值点. 相似文献
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Duren Peter; Gallardo-Gutierrez Eva A.; Montes-Rodriguez Alfonso 《Bulletin London Mathematical Society》2007,39(3):459-466
An analogue of the PaleyWiener theorem is developed forweighted Bergman spaces of analytic functions in the upper half-plane.The result is applied to show that the invariant subspaces ofthe shift operator on the standard Bergman space of the unitdisk can be identified with those of a convolution Volterraoperator on the space L2(+, (1/t)dt). 相似文献
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Let MS be the universal maximal operator over unit vectors ofarbitrary directions. This operator is not bounded in L2(R2).We consider a sequence of operators over sets of finite equidistributeddirections converging to MS. We provide a new proof of N. Katz'sbound for such operators. As a corollary, we deduce that MSis bounded from some subsets of L2 to L2. These subsets arecomposed of positive functions whose Fourier transforms havea logarithmic decay or which are supported on a disc. 1991 MathematicsSubject Classification 42B25. 相似文献
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Using the BMO-H1 duality (among other things), D. R. Adams provedin [1] the strong type inequality
whereC is some positive constant independent of f. Here M is theHardyLittlewood maximal operator in Rn, H is the -dimensionalHausdorff content, and the integrals are taken in the Choquetsense. The Choquet integral of 0 with respect to a set functionC is defined by
Precise definitionsof M and H will be given below. For an application of (1) tothe Sobolev space W1, 1 (Rn), see [1, p. 114]. The purpose of this note is to provide a self-contained, directproof of a result more general than (1). 1991 Mathematics SubjectClassification 28A12, 28A25, 42B25. 相似文献
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** Email: sano{at}cc.kagoshima-u.ac.jp This paper is concerned with the dynamical analysis of parallel-flowheat exchanger equations with observation at the outlet of tube/controlat the inlet of tube. The parallel-flow heat exchanger equationis super-stable under zero boundary condition. The system canbe described by an unbounded operator of lower triangular formthrough a variable transformation. By calculating a C0-semigroupgenerated by the operator, it is shown that the system is observableif both fluid temperatures are measured at the outlet, and thatthe system is observable with respect to the non-negative coneof the state space if either of them is measured at the outlet.Moreover, it is shown that the system is reachable if both fluidtemperatures are controlled at the inlet, and that the systemis reachable with respect to the non-negative cone of the statespace if either of them is controlled at the inlet. 相似文献
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An AW*-algebra is a W*-algebra if and only if it is normal andhas a large W* corner. Analogous results are proved for therepresentation of AW*-algebras as operator algebras on AW*-modules. 相似文献