共查询到20条相似文献,搜索用时 15 毫秒
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《Quaestiones Mathematicae》2013,36(3-4):311-318
Abstract We obtain some results concerning the notions of hypercyclicity and supercyclicity for continuous homogeneous polynomial maps in Banach spaces. We also present a generalization of a theorem due to Beauzamy concerning the existence of orbits tending to infinity for continuous linear operators with spectral radius > 1. 相似文献
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Qianglian Huang & Shuangyun Gao 《分析论及其应用》2012,28(2):146-155
Utilizing the stability characterizations of generalized inverses of linear operator, we investigate the existence of generalized resolvent of linear pencils in Banach spaces. Some practical criterions for the existence of generalized resolvents of the linear pencil λ→ T λ S are provided and an explicit expression of the generalized resolvent is also given. As applications, the characterization for the Moore-Penrose inverse of the linear pencil to be its generalized resolvent and the existence of the generalized resolvents of linear pencils of finite rank operators, Fredholm operators and semi-Fredholm operators are also considered. The results obtained in this paper extend and improve many results in this area. 相似文献
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本文给出了Hilbert变换在Banach空间值Hardy空间HB^1(R)上的有界性。 相似文献
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SHEN Yuliang 《数学年刊B辑(英文版)》2001,22(1):75-84
51. IntroductionThe convexity of Banach spaces is an important topic in functional analysis and playsan importals role in indnite dimensional holomorphy. In order to study the geometricproperties of a Banach spacet Clarksonl3] and Krein (independently) introduced the veryimportallt class of strict convex spaces. In the same paper [3], Clarkson also introduced thestronger notion of uniform convexity. Since Clarkson's paper many authors have definedand studied the classes of Banach spaces lyi… 相似文献
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《Quaestiones Mathematicae》2013,36(3-4):247-260
Abstract Let X be a Banach space. A linear subspace of X is called an operator range if it coincides with the range of a bounded linear operator defined on some Banach space. The paper studies disjointness and inclusion properties of various types of operator ranges in a separable infinite dimensional Banach space X. One of the main results is the following: Let E be a non-closed operator range in X. Then X contains a non-closed dense operator range R with the properties E∩= {0}, and R is decomposable, i.e. R = M + N where M,N are closed and infinite dimensional and M ∩ N = {0} (Theorem 6.2). 相似文献
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GUO Dajun 《数学年刊B辑(英文版)》1999,20(4):435-446
51.IntroductionIn[1,Section3.3])wehavediscussedtheinitialvalueproblem(IVP)forfirstorderintegrthdtherentialequationsofVolterratroeoninfiniteintervalJ=[O,oo)inarealBanachspaceEbymeansoffixedpoillttheory.Now,inthispaper,weshallinvestigatetheIVPforn-thordersuchequationsbymeansofcompletelydtherentmethod,thatis,byestablishingacomparisonresultandusingthemonotoneiterativetecdrique.ConsidertheIVPforn-thordernonlinearilltegrthdifferelitialequationofVolterratypeinE:whereJ=[O,oo),uiEE(i=O,1,'jn… 相似文献
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Zhou Feng 《数学年刊B辑(英文版)》1998,19(3):249-254
§1.IntroductionLetEbearealBanachspace,notnecesarilyreflexive.LetΦ,Ψ:E→]-∞,∞]betwolowersemicontinuousconvexfunctions.Wedenote... 相似文献
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《Quaestiones Mathematicae》2013,36(3-4):479-481
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《数学物理学报(B辑英文版)》2020,(3)
This article is committed to deal with measure of non-compactness of operators in Banach spaces. Firstly, the collection C(X)(consisting of all nonempty closed bounded convex sets of a Banach space X endowed with the uaual set addition and scaler multiplication) is a normed semigroup, and the mapping J from C(X) onto F(?) is a fully order-preserving positively linear surjective isometry, where ? is the closed unit ball of X*and F(?) the collection of all continuous and w*-lower semicontinuous sublinear functions on X*but restricted to ?. Furthermore, both ■ and ■ are Banach lattices and EK is a lattice ideal of EC. The quotient space EC/EK is an abstract M space, hence,order isometric to a sublattice of C(K) for some compact Haudorspace K, and(FQJ)C which is a closed cone is contained in the positive cone of C(K), where Q : E_C → E_C/E_K is the quotient mapping and F : E_C/E_K → C(K) is a corresponding order isometry. Finally, the representation of the measure of non-compactness of operators is given: Let B_X be the closed unit ball of a Banach space X, then■ 相似文献
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Clarkson不等式与Banach空间几何 总被引:2,自引:2,他引:0
我们证明了Banach空间X是Clarkson p型(q余型)当且仅当X是一个特殊的p一致光滑空间(q-一致凸空间(),我们还找到刻划型(余型)的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。 相似文献
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We present an existence theorem for at least one weak solution for a coupled system of integral equations of Volterra type in a reflexive Banach spaces relative to the weak topology. 相似文献
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1 IntroductionDiscrete reaction--diffusion type partial difference equations llave recentlybeen introduced by a number of authors as modeIs for the study of spatiotem-poral chaos (see e.g. [2,3j). Stability criteria have also been derived fOr suchequatioIls which invoIve two time-level processes (see e.g. [1l) as well as three-level processes (see e.g. [9]). In this paper, we will study no11linear three--levc1partia1 diffcrence equations in an abstract setting and derive stability criteriafo… 相似文献
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本文利用“强极小锥”的概念,获得了Banach空间中非线性脉冲Volterra型积分方程整体解的存在性定理,改进了现有文献中的某些结果. 相似文献
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Huang Falun 《数学年刊B辑(英文版)》1989,10(3):332-340
In this paper the author proves a new fundamental lemma of Hardy-Lebesgne class
$\[{H^2}(\sigma )\]$ and by this lemma obtains some fundamental results of exponential stability of $\[{C_0}\]$-semigroup of bounded linear operators in Banach spaces. Specially, if $\[{\omega _s} = \sup \{ {\mathop{\rm Re}\nolimits} \lambda ;\lambda \in \sigma (A) < 0\} \]$ and $\[\sup \{ \left\| {{{(\lambda - A)}^{ - 1}}} \right\|;{\mathop{\rm Re}\nolimits} \lambda \ge \sigma \} < \infty \]$ , where \[\sigma \in ({\omega _s},0)\]) and A is the infinitesimal generator of a $\[{C_0}\]$-semigroup in a Banach space $X$, then $\[(a)\int_0^\infty {{e^{ - \sigma t}}\left| {f({e^{tA}}x)} \right|} dt < \infty \]$, $\[\forall f \in {X^*},x \in X\]$; (b) there exists $\[M > 0\]$ such that $\[\left\| {{e^{tA}}x} \right\| \le N{e^{\sigma t}}\left\| {Ax} \right\|\]$, $\[\forall x \in D(A)\]$; (c) there
exists a Banach space $\[\hat X \supset X\]$ such that $\[\left\| {{e^{tA}}x} \right\|\hat x \le {e^{\sigma t}}\left\| x \right\|\hat x,\forall x \in X.\]$. 相似文献
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61. Introduction and PreliminariesLet C be a nonempty subset Of a Banal spare X. Then a mapping T: C -- C is saidto be a LiPSdrizian maPPing if, for ear integer n 2 1, there eallts a constant km > 0' such that Ilaal ~ chill S k.llx ~ all for all ale E C. A Lipschitzian mapping T is saidto be ~ k-LiPSdszian if km = k for all n 2 1, nonerpansive if km = 1 for alln 2 1, eleCtively. Moreover, a maPPing T: C - C is called asymptotically regularll'191if Asllgu 'z ~ chill = 0 for all 2 E… 相似文献
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本文主要研究了 Banach 空间上交换算子组的张量积以及 Banach 代数的张量积中交换元组的 Taylor 联合谱,推广了 Vasilescu,F.H.及 Wrobel,V.等人结果。 相似文献
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Liu Peide 《数学年刊B辑(英文版)》1992,13(2):167-179
The aim of this paper is establishing some inequalities of several operators on Banach-space-valued martingales and using them to give some characterizations of geometrical properties of Banach spaces. In particular, the Φ-function nequalitities of sharp operators f_p~#, f_p~#, p-variation operators W_p, W_p and the martingale tranform operator T_v are discussed. It is proved that the boundedness of these operators characterizes the smoothness, convexity and UMD-property of Banach spaces. 相似文献