共查询到20条相似文献,搜索用时 15 毫秒
1.
Christian Le Merdy 《Complex Analysis and Operator Theory》2014,8(3):665-681
Let $T:X\rightarrow X$ be a power bounded operator on Banach space. An operator $C:X\rightarrow Y$ is called admissible for $T$ if it satisfies an estimate $\sum _k\Vert CT^k(x)\Vert ^2\,\le M^2\Vert x\Vert ^2$ . Following Harper and Wynn, we study the validity of a certain Weiss conjecture in this discrete setting. We show that when $X$ is reflexive and $T$ is a Ritt operator satisfying a appropriate square function estimate, $C$ is admissible for $T$ if and only if it satisfies a uniform estimate $(1-\vert \omega \vert ^2)^{\frac{1}{2}}\Vert C(I-\omega T)^{-1}\Vert \,\le K\,$ for $\omega \in \mathbb{C }$ , $\vert \omega \vert <1$ . We extend this result to the more general setting of $\alpha $ -admissibility. Then we investigate a natural variant of admissibility involving $R$ -boundedness and provide examples to which our general results apply. 相似文献
2.
We study a 22 operator matrix associated with a closed densely
defined operator. Among others, the selfadjointness of a closed symmetric
operator and the strong commutativity of two (unbounded) self-adjoint operators
are characterized in terms of the related operator matrices. We propose
a definition of strong commutativity for closed symmetric operators.
Submitted: November 8, 2001 相似文献
3.
Na Qiyuan 《数学年刊B辑(英文版)》1990,11(4):403-409
Some characterizations of the conditional expectation operators on Lebesgue-Bochner spaces L_p(\mu,X) are given, where $1\leq p<\infinity,p\neq 2$. Also an example is given to show that the characterizations of the conditional expectation operators on L_p(\mu, X) are different from that on L_p(\mu).Finally, a representation of the constant-preserving contractive projection on spaces L_p(\mu, X) is got when 0
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4.
Let μ, v ∈ [0, 1) be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg :βμ→βv is bounded and compact. 相似文献
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Invariant and Hyperinvariant Subspace Lattices of Operators $$J^\alpha \otimes B$$ in Sobolev Spaces
Mathematical Notes - Let . 相似文献
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We show that positive isometric averaging operators on the sequence space \({\ell^2(\mathbb{Z}, \mu)}\) are determined by very subtle arithmetic conditions on \({\mu}\) (even for very simple examples), contrary to what happens in the continuous case \({L^2({\mathbb{R}}^+)}\), where any possible average value is realized by a suitable positive isometry. 相似文献
8.
Suppose φ is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator Cφ: Cφf = f °φ, for all f ∈ X. In this paper, the boundedness and compactness of the composition operators from α-Bloch spaces into QK(p,q) and QK,0(p,q) spaces are discussed, where 0 〈 α 〈 ∞. 相似文献
9.
In this work we characterize the bounded and the compact weighted composition operators from the space $H^\infty $ of bounded analytic functions on the open unit disk into the Zygmund space and the little Zygmund space. We also provide boundedness and compactness criteria of the weighted composition operators from the Bloch space into the little Zygmund space. In particular, we show that the bounded operators between these spaces are necessarily compact. 相似文献
10.
卷积型Calder\'{o}n-Zygmund算子的新算法 总被引:1,自引:0,他引:1
Beylkin-Coifman-Rokhlin
(B-C-R)算法表明算子通常可用$2n$维小波来分析, 而本文用
基于$n$维小波来引入一种新方法考虑卷积型 Calder\'{o}n-Zygmund
(C-Z)算子. 利用此方法来研究算子的逼近, 此逼近算法不仅比 B-C-R
算法简单而且有更快的逼近速度. 还证明了 H\"{o}rmander
条件能够保证算子在 Besov 空间$\dot{B}_p^{0,q}\ (1\leq p,\, q
\leq\infty)$ 和 Triebel--Lizorkin 空间$\dot{F}_p^{0,q}(1
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11.
We prove that on smooth bounded pseudoconvex Hartogs domains in \(\mathbb {C}^2\) compactness of the \(\overline{\partial }\)-Neumann operator is equivalent to compactness of all Hankel operators with symbols smooth on the closure of the domain. 相似文献
12.
设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画;
然后
分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的
微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为
$A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件. 相似文献
13.
Yusuf DANISMAN 《数学年刊B辑(英文版)》2017,38(4):1019-1036
The L-factor of irreducible x1×x2(×)σ defined by Piatetski-Shapiro is computed by using non-split Bessel functional. 相似文献
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An Accelerated Algorithm Involving Quasi-$\phi$-Nonexpansive Operators for Solving Split Problems 下载免费PDF全文
Bashir Ali Aisha Aminu Adam Abubakar Adamu 《Journal of Nonlinear Modeling and Analysis》2023,5(1):54-72
In this paper, an algorithm of inertial type for approximating solutions of split equality fixed point problems involving quasi-$\phi$-nonexpansive maps is proposed and studied in the setting of certain real Banach spaces. Weak and strong convergence theorems are proved under some conditions. Some applications of the theorems are presented. The results presented extend and improve some existing results. Finally, some numerical illustrations are presented to support our theorems and their applications. 相似文献
16.
Let \(C_1(H)\) denote the space of all trace class operators on an arbitrary complex Hilbert space H. We prove that \(C_1(H)\) satisfies the \(\lambda \)-property, and we determine the form of the \(\lambda \)-function of Aron and Lohman on the closed unit ball of \(C_1(H)\) by showing that for every a in \({C_1(H)}\) with \(\Vert a\Vert _1 \le 1\). This is a non-commutative extension of the formula established by Aron and Lohman for \(\ell _1\).
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$$\begin{aligned} \lambda (a) = \frac{1 - \Vert a\Vert _1 + 2 \Vert a\Vert _{\infty }}{2}, \end{aligned}$$
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Some combinatorial and probabilistic estimates motivated by earlier works due to S. Kwapien and C. Schütt are proved. We study these estimates in the general setting of rearrangement invariant function and sequence spaces and identify the class of function spaces in which such estimates hold. We demonstrate the sharpness of our results and present some applications, one of which is an alternative proof of a familiar Raynaud–Schütt theorem describing symmetric subspaces in \({L_1}\). 相似文献
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