共查询到19条相似文献,搜索用时 906 毫秒
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本文刻划了Hardy空间或Bergman空间上符号为有限Blaschke积的Toeplitz算子的换位,并讨论了其完全可约性。 相似文献
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在自反Banach空间上一个有界线性算子是(B)型良性有界的当且仅当它的共扼算子也是(B)型的。但在非自反Banach空间上这种性质不成立。本文证明在一大类非自反Banach空间上总存在一个(B)型良性有界线性算子,它的共扼算子不是(B)型的。同时也证明了在具有基的Banach空间上,任何P型基序列一定有一个子序弄能够扩张成该空间的一个基。 相似文献
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为改造正线性算子以提高其逼近阶,本文利用有限振荡核方法,从常见的Fejer算子出发,构造出一种莼性多项式算子Ln^(m)(f;x),称F-B算子,它的表达式具有良好的递推性能;通过对其收敛性和饱和性的讨论,证得F-B算子对充分光滑函数的逼近阶可达O(1/n^2m+1),优于Butzer与Stark的结果(O(1/n^4)),并包含Baskakov的结果(O(1/n^3)与O(1/n^5))为其特例 相似文献
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一类扰动半群生成元的谱分布及其应用 总被引:5,自引:0,他引:5
本文研究了扰动半群生成元A=B+K在带形区域S(B)〈Reλ〈ω(B)+‖K‖内的谱分布,目的是寻找A在带形区域中只分布孤立的有限重本征值以及可能的聚点只分布在直线Reλ=S(B)上的条件。作为结论的直接应用,本文非常简洁地证明了中子迁移算子的相关结论。 相似文献
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C~m空间中非线性Lipschitz连续算子的定量性质 总被引:4,自引:0,他引:4
在有限维复Banach空间Cm中,全体Lipschitz连续算子构成一赋半范的非线性算子空间L(Cm).本文研究L(Cm)中非线性算子的定量性质,包括:L(Cm)中可逆算子到不可逆算子集合的逼近距离、L(Cm)中算子乘幂压缩的逆问题以及L(Cm)中算子的数值值域与谱集的联系,文中所得结果推广了线性算子理论中许多著名结论. 相似文献
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证得:在Banach空间中,相对紧集上的恒等算子可由一列有限秩连续拟线性投影算子一致逼近.由此得到:线性算子为紧线性算子必须且仅须它可由一列有限秩连续齐性算子一致逼近. 相似文献
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讨论了加权Bergman空间AP()(1<p<∞)上的Toeplitz算子证明了Toeplitz算子的有限乘积的有限和是紧算子当区仅当其Berezin变换在边界趋向于零. 相似文献
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解析函数的Banach空间上之复合算子 总被引:2,自引:0,他引:2
本文研究了一类解析函数的Banach空间X上之复合算子,这类空间包含了Bloch空间,并且可看作Bergman空间L1a(D)中具有原子分解的解析函数的对偶空间.我们刻划了这类空间上紧复合算子及Fredholm复合算子的特征,此外,还研究了具有闭值域的复合算子. 相似文献
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本文研究了紧致齐性空间上的Riesz位势算子与Bessel位势算子,Riesz变换与Bessel变换,给出了上述算子对应的核函数的具体构造并证明了Riesz变换与Bessel变换作为奇异积分算子的H ̄p有界性,p>0。 相似文献
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Xuanhao Ding 《Journal of Mathematical Analysis and Applications》2006,320(1):464-481
A limit theorem is established for a finite sum of finite products of Toeplitz operators on the Hardy space of the polydisk. As a consequence we show that the product of six Toeplitz operators with pluriharmonic symbols is compact iff the product equals zero iff one of these Toeplitz operators equals zero. 相似文献
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Kunyu Guo 《Journal of Functional Analysis》2005,218(1):1-53
A generalized area function associated with a finite sum of finite products of Toeplitz operators is introduced. A distribution function inequality is established for the generalized area function. By using the distribution function inequality, we characterize when a finite sum of finite products of Toeplitz operators on the Hardy space is a compact perturbation of a Toeplitz operator. 相似文献
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On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. 相似文献
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In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator. 相似文献
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Young Joo Lee 《Journal of Mathematical Analysis and Applications》2009,357(2):504-515
On the Dirichlet space of the unit disk, we consider a class of operators which contain finite sums of products of two Toeplitz operators with harmonic symbols. We give characterizations of when an operator in that class is zero or compact. Also, we solve the zero product problem for products of finitely many Toeplitz operators with harmonic symbols. 相似文献
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In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator. 相似文献
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We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols.
We show that in this context, the situation is different from the case of harmonic Toeplitz operators.
Submitted: July 23, 2007. Accepted: December 4, 2007. 相似文献