共查询到16条相似文献,搜索用时 109 毫秒
1.
2×2阶上三角型算子矩阵的Moore-Penrose谱 总被引:1,自引:1,他引:1
设$H_{1}$和$H_{2}$是无穷维可分Hilbert空间. 用$M_{C}$表示$H_{1}\oplusH_{2}$上的2$\times$2阶上三角型算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\\end{array}\right)$. 对给定的算子$A\in{\mathcal{B}}(H_{1})$和$B\in{\mathcal{B}}(H_{2})$,描述了集合$\bigcap\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$与$\bigcup\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$,其中$\sigma_{M}(\cdot)$表示Moore-Penrose谱. 相似文献
2.
设$\mathcal{A}$ 是一个Abel范畴,且 $(\mathcal{X}, \mathcal{Z},\mathcal{Y})$ 是一个完全遗传余挠三元组.介绍 $\mathcal{A}$ 的 $n$-$\mathcal{Y}$-余倾斜子范畴的定义,并给出 $n$-$\mathcal{Y}$-余倾斜子范畴的一个刻画,类似于 $n$-余倾斜模的 Bazzoni 刻画.作为应用,证明了在一个几乎 Gorenstein 环 $R$ 上, 如果 $\mathcal{GP}$ 是 $n$-$\mathcal{GI}$-余倾斜的, 那么 $R$ 是一个 $n$-Gorenstein 环, 其中 $\mathcal{GP}$ 表示 Gorenstein 投射 $R$-模组成的子范畴且 $\mathcal{GI}$ 表示 Gorenstein 内射 $R$-模组成的子范畴. 进而, 研究 任意环$R$上的$n$-余星子范畴, 以及关于余挠三元组 $(\mathcal{P}, R$-Mod, $\mathcal{I})$ 的 $n$-$\mathcal{I}$-子范畴与 $n$-余星子范畴之间的关系, 其中 $\mathcal{P}$ 表示投射左 $R$-模组成的子范畴且 $\mathcal{I}$ 表示内射左 $R$-模组成的子范畴. 相似文献
3.
Yao Yunlong 《数学年刊B辑(英文版)》1985,6(1):27-34
Let V and H be two Hilbert spaces satisfying the imbedding relation V\subset H. Let $[ - \mathscr{A}:V \to V''\]$ be the linear operator determined by a(u, v) = <\mathscr{A}u, v> for u, v\in V, where a(u, v) is a continuous sesquilinear form on V satisfying
$a(u, u)+\lambda|u|_H^2\geq c||u||_V^2$
for u\in V and some \lambda \in R and c>0.
In this paper it is proved that —\mathscr{A} is the generator of an analytic C_0-semigroup on V''. Furthermore, if b(u, v) is a continuous sesquilinear form on HxV and \mathscr{B}: H\rightarrow V, the linear operator determined by b(u, v) = (\mathscr{B}u, v) for u, v\in V, then —\mathscr{A}—mathscr{B} is also the generator of C_0-semigroup on V''.
Also, similar results are proved on “inserted” spaces V_\theta(\theta \geq -1) which are determined by the spectrum system of \mathscr{A}. 相似文献
4.
设$\overrightarrow{G}$ 是一个强连通双圈有向图, $A(\overrightarrow{G})$是其邻接矩阵.设$D(\overrightarrow{G})$ 是$\overrightarrow{G}$的顶点出度的对角矩阵, $Q(\overrightarrow{G})=D(\overrightarrow{G})+A(\overrightarrow{G})$是$\overrightarrow{G}$ 的无符号拉普拉斯矩阵. $Q(\overrightarrow{G})$的谱半径称为$\overrightarrow{G}$的无符号拉普拉斯谱半径.在这篇文章中, 确定了在所有强连通双圈有向图中达到最大或最小无符号拉普拉斯谱半径的唯一有向图. 此外,还证明了任意一个强连通双圈有向图是由它的无符号拉普拉斯谱所确定的. 相似文献
5.
徐宁 《数学年刊A辑(中文版)》2013,34(3):269-278
设$H(\mathbb{B})$为单位球上全纯函数类,研究了单位球上 Zygmund 空间到 Bloch 空间上径向导数算子$\Re$与积分型算子$I_\varphi^g$乘积的有界性和紧性,
这里
$$
I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B},
$$
其中$g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ 是$\mathbb{B}$上全纯自映射. 相似文献
6.
In this paper, we consider the generalized Weinstein operator $\Delta_{W}^{d,\alpha,n}$, we introduce new Sobolev-Weinstein spaces denoted $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1}),$ $s\in\mathbb{R},$ associated with the generalized Weinstein operator and we investigate their properties. Next, as application, we study the extremal functions on the spaces $\mathscr H_{\alpha,d,n}^{s}(\mathbb{R}_{+}^{d+1})$ using the theory of reproducing kernels. 相似文献
7.
在上半复平面$\mathbb{H}$上给定双曲测度$dxdy/y^{2}$, 群$G={\rm PSL}_{2}(\mathbb{R})$ 在$\mathbb{H}$上的分式线性作用导出了$G$在Hilbert空间$L^{2}(\mathbb{H}, dxdy/y^{2})$上的酉表示$\alpha$. 证明了交叉积 $\mathcal{R}(\mathcal{A}, \alpha)$是$\mathrm{I}$型von Neumann代数, 其中$\mathcal{A}= \{M_{f}:f\in L^{\infty}(\mathbb{H},dxdy/y^{2} )\}$. 具体地, 交叉积代数$\mathcal{R}(\mathcal{A}, \alpha)$与von Neumann代数$\mathcal{B}(L^{2}(P, \nu))\overline{\otimes}\mathcal{L}_{K}$是*-同构的, 其中$\mathcal{L}_{K}$是$G$中子群 $K$的左正则表示生成的群von Neumann代数. 相似文献
8.
图$G$的$(\mathcal{O}_{k_1}, \mathcal{O}_{k_2})$-划分是将$V(G)$划分成两个非空子集$V_{1}$和$V_{2}$, 使得$G[V_{1}]$和$G[V_{2}]$分别是分支的阶数至多$k_1$和$k_2$的图.在本文中,我们考虑了有围长限制的平面图的点集划分问题,使得每个部分导出一个具有有界大小分支的图.我们证明了每一个围长至少为6并且$i$-圈不与$j$-圈相交的平面图允许$(\mathcal{O}_{2}$, $\mathcal{O}_{3})$-划分,其中$i\in\{6,7,8\}$和$j\in\{6,7,8,9\}$. 相似文献
9.
该文首先研究具有脉冲的线性Dirichlet边值问题
$\left\{
\begin{array}{ll}
x'(t)+a(t)x(t)=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=c_{k}x(\tau_{k}),\ \Delta x'(\tau_{k})=d_{k}x(\tau_{k}), \ x(0)=x(T)=0,
\end{array}
\right. (k=1,2\cdots,m)
$
给出该Dirichlet边值问题仅有零解的两个充分条件, 其中$a:[0,T]\rightarrow R$, $c_{k}, d_{k}, k=1,2,$ $\cdots,m$是常数, 该文首先研究具有脉冲的线性Dirichlet边值问题
$$\left\{
\begin{array}{ll}
x'(t)+a(t)x(t)=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=c_{k}x(\tau_{k}),\ \Delta x'(\tau_{k})=d_{k}x(\tau_{k}), \ x(0)=x(T)=0,
\end{array}
\right. (k=1,2\cdots,m)
$$
给出该Dirichlet边值问题仅有零解的两个充分条件, 其中$a:[0,T]\rightarrow R$, $c_{k}, d_{k}, k=1,2,$ $\cdots,m$是常数, $0<\tau_{1}<\tau_{2}\cdots<\tau_{m}<T$为脉冲时刻. 其次利用上面的线性边值问题仅有零解这个性质和Leray-Schauder度理论, 研究具有脉冲的非线性Dirichlet边值问题
$$\left\{
\begin{array}{ll}
x'(t)+f(t,x(t))=0, t\neq \tau_{k}, \ \Delta x(\tau_{k})=I_{k}(x(\tau_{k})), \ \Delta x'(\tau_{k})=M_{k}(x(\tau_{k})), \ x(0)=x(T)=0
\end{array}
\right. (k=1,2\cdots,m)
$$ 解的存在性和唯一性, 其中 $f\in C([0,T]\times
R,R)$, $I_{k},M_{k}\in C(R, R),k=1,2,\cdots,m$.
该文主要定理的一个推论将经典的Lyaponov不等式比较完美地推广到脉冲系统. 相似文献
10.
本文研究了单位圆盘上从$L^{\infty}(\mathbb{D})$空间到Bloch型空间 $\mathcal{B}_\alpha$ 一类奇异积分算子$Q_\alpha, \alpha>0$的范数, 该算子可以看成投影算子$P$ 的推广,定义如下$$Q_\alpha f(z)=\alpha \int_{\mathbb{D}}\frac{f(w)}{(1-z\bar{w})^{\alpha+1}}\d A(w),$$ 同时我们也得到了该算子从 $C(\overline{\mathbb{D}})$空间到小Bloch型空间$\mathcal{B}_{\alpha,0}$上的范数. 相似文献
11.
令A是阿贝尔范畴, T是A的一个自正交子范畴, 且T中每个对象均有有限投射维数和内射维数. 假设左Gorenstein子范畴lG(T)等于T的右正交类,且右Gorenstein子范畴rG(T)等于T的左正交类,我们证明了Gorenstein子范畴$G(T)$等于T的左正交类与T的右正交类之交,并且证明了它们的稳定范畴三角等价于A关于T的相对奇点范畴.作为应用,令$R$是有有限左自内射维数的左诺特环, $_RC_s$是半对偶化双模,且所有内射左$R$-模的平坦维数的上确界有限, 我们证明了 若$\mbox{}_RC$有有限内射(平坦)维数且$C$的右正交类包含$R$,则存在从$C$-Gorenstein投射模与关于$C$的Bass类的交到关于$C$-投射模的相对奇点范畴间的三角等价,推广了某些经典的结果. 相似文献
12.
Fatemah Ayatollah Zadeh Shirazi Amir Fallahpour Mohammad Reza Mardanbeigi & Zahra Nili Ahmadabadi 《分析论及其应用》2022,38(1):110-120
For a finite discrete topological space $X$ with at least two elements, a nonempty set $\Gamma$, and a map $\varphi:\Gamma \to \Gamma$, $\sigma_{\varphi}:X^{\Gamma} \to X^{\Gamma}$with $\sigma_{\varphi}((x_{\alpha})_{\alpha \in \Gamma})=(x_{\varphi(\alpha)})_{\alpha \in \Gamma}$ (for $(x_{\alpha})_{\alpha \in \Gamma} \in X^{\Gamma}$) is a generalized shift. In this text for $\mathcal{S} = \{\sigma_{\varphi}:\varphi \in \Gamma^{\Gamma}\}$ and $\mathcal{H}=\{\sigma_{\varphi}:\Gamma \xrightarrow{\varphi} \Gamma$ is bijective$\}$ we study proximal relations of transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$. Regarding proximal relation we prove: $$P(\mathcal{S}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \exists \beta \in \Gamma (x_{\beta} = y_{\beta})\}$$and $P(\mathcal{H}, X^{\Gamma} ) \subseteq \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\beta \in \Gamma : x_{\beta} = y_{\beta}\}$ is infinite$\}$ $\cup\{($ $x,x) : x \in \mathcal{X}\}$. Moreover, for infinite $\Gamma$, both transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$ are regionally proximal, i.e., $Q(\mathcal{S}, X^{\Gamma}) = Q(\mathcal{H}, X^{\Gamma} ) = X^{\Gamma} \times X^{\Gamma}$, also for sydetically proximal relation we have $L(\mathcal{H}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\gamma ∈ \Gamma :$ $x_{\gamma} \neq y_{\gamma}\}$ is finite$\}$. 相似文献
13.
记DC为单位圆盘,B~k C~k为开欧氏单位球,Ω是C~k(或C)中的域.记H_n(D,Ω)为满足一定条件的全纯映照族(或函数族)的全体.作者证明了若,∈Hn(D,D),则|f′(z)|≤(n|z|~(n-1))/(1-|z|~(2n))(1-|f|(z|~2),z∈DD同时,对Hn(D,B~k)中映照的模也得到类似的结果.该结论推广了Pavlovic的相应结果. 相似文献
14.
Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M(D,V,F) a 3×3 upper triangular operator matrix acting on Hi +H2+ H3 of theform M(D,E,F)=(A D F 0 B F 0 0 C).For given A ∈ B(H1), B ∈ B(H2) and C ∈ B(H3), the sets ∪D,E,F^σp(M(D,E,F)),∪D,E,F ^σr(M(D,E,F)),∪D,E,F ^σc(M(D,E,F)) and ∪D,E,F σ(M(D,E,F)) are characterized, where D ∈ B(H2,H1), E ∈B(H3, H1), F ∈ B(H3,H2) and σ(·), σp(·), σr(·), σc(·) denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively. 相似文献
15.
Multiple sign-changing solutions for a class of semilinear elliptic equations in $\mathbb{R}^{N}$ 下载免费PDF全文
In this paper, we study the following semilinear elliptic equations $$-\triangle u+V(x)u=f(x,u), \ \ x\in \mathbb{R}^{N},$$ where $V\in C(\mathbb{R}^{N}, \mathbb{R})$ and $f\in C(\mathbb{R}^{N}\times\mathbb{R}, \mathbb{R})$. Under some suitable conditions, we prove that the equation has three solutions of mountain pass type: one positive, one negative, and sign-changing. Furthermore, if $f$ is odd with respect to its second variable, this problem has infinitely many sign-changing solutions. 相似文献
16.
Let (CΩ△) be a left triangulated category with a fully faithful endofunctor.We show a triangle-equivalence (S(C),△) ~=(S(C),△),where (S(C)△,) denotes the stabilization of the idempotent completion of (C,△) and (S(C),△) denotes the idempotent completion of the stabilization of (C,△). 相似文献