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1.
研究了C^n中有界强拟凸Ω上Bergman空间A^p(Ω)上的复合算子的有界性、紧性,给出了复合算子Cψ:A^p(Ω)→A^p(Ω)紧性的一个完整刻划。 相似文献
2.
Zhi Jie Jiang 《Applied mathematics and computation》2010,217(7):3522-3530
We characterize the compactness of differences of weighted composition operators from the weighted Bergman space , 0 < p < ∞, α > −1, to the weighted-type space of analytic functions on the open unit disk D in terms of inducing symbols and . For the case 1 < p < ∞ we find an asymptotically equivalent expression to the essential norm of these operators. 相似文献
3.
We find a lower bound for the essential norm of the difference of two composition operators acting on H 2(BN ) or As2 (BN ) (s > 1). This result plays an important role in proving a necessary and sufficient condition for the difference of linear fractional composition operators to be compact, which answers a question posed by MacCluer and Weir in 2005. 相似文献
4.
María J. Martín 《Journal of Functional Analysis》2006,238(1):298-312
We observe that a formula for the adjoint of a composition operator, known only for special symbols in some spaces of analytic functions, actually holds for every admissible symbol and in any Hilbert space of analytic functions with reproducing kernels. Along with some new results, all known formulas for the adjoint obtained so far follow easily as a consequence, some in an improved form. 相似文献
5.
Sean Effinger-Dean 《Journal of Mathematical Analysis and Applications》2006,324(2):1062-1072
We compute the norms of composition operators with rational symbols that satisfy certain properties, extending Christopher Hammond's methods on operators with linear fractional symbols. This leads to a host of new examples of composition operators whose norms are calculable. 相似文献
6.
Christopher Hammond Jennifer Moorhouse 《Journal of Mathematical Analysis and Applications》2008,341(1):626-639
Building on techniques developed by Cowen and Gallardo-Gutiérrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space H2. We consider some specific examples, comparing our formula with several results that were previously known. 相似文献
7.
江治杰 《纯粹数学与应用数学》2010,26(6):984-991
通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。 相似文献
8.
Linear relations in the Calkin algebra for composition operators 总被引:1,自引:0,他引:1
Thomas Kriete Jennifer Moorhouse 《Transactions of the American Mathematical Society》2007,359(6):2915-2944
We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?
9.
In this paper, we prove that a composition operator onH
p
(B) is Fredholm if and only if it is invertible if and only if its symbol is an automorphism onB, and give the representation of the spectra of a class of composition operators. In addition, using composition operator,
we discuss intertwining Toeplitz operators.
Supported by NNSF and PDSF 相似文献
10.
11.
Erno Saukko 《Journal of Mathematical Analysis and Applications》2011,381(2):789-798
We obtain estimates for the norm and essential norm of the difference of two composition operators between certain Bergman spaces. In particular, a necessary and sufficient condition for boundedness and compactness of the operator is established. Finally, we give a sufficient condition for boundedness and compactness of the difference operator between Hardy spaces. 相似文献
12.
Compact composition operators on the Bloch space in polydiscs 总被引:1,自引:0,他引:1
Let Un be the unit polydisc of ℂn and φ=(φ1, ⋯, φ
n
) a holomorphic self-map of Un. As the main result of the paper, it shows that the composition operator C is compact on the Bloch space β(Un) if and only if for every ε > 0, there exists a δ > 0, such that
whenever dist(φ(z), ∂U
n
)<δ. 相似文献
13.
Building on techniques developed by Cowen (1988) [3] and Nazarov–Shapiro (2007) [10], it is shown that the adjoint of a composition operator, induced by a unit disk-automorphism, is not strongly asymptotically Toeplitz. This result answers Nazarov–Shapiro’s question in Nazarov and Shapiro (2007) [10]. 相似文献
14.
Sam Elliott 《Journal of Functional Analysis》2009,256(12):4162-4186
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known necessary condition for the boundedness of such operators, and use it to provide a complete classification of the bounded composition operators with rational symbol. We then consider some specific examples, comparing our formulae with each other, and with other easily deduced formulae for simple cases. 相似文献
15.
We will consider the problem of which the products of composition and analytic Toeplitz operators would be bounded or compact on the Hardy space H2 and the Bergman space La2. 相似文献
16.
Compact composition operators on the Smirnov class 总被引:1,自引:0,他引:1
Jun Soo Choa Hong Oh Kim Joel H. Shapiro 《Proceedings of the American Mathematical Society》2000,128(8):2297-2308
We show that a composition operator on the Smirnov class is compact if and only if it is compact on some (equivalently: every) Hardy space for . Along the way we show that for composition operators on both the formally weaker notion of boundedness, and a formally stronger notion we call metric compactness, are equivalent to compactness.
17.
Valentin Matache 《Proceedings of the American Mathematical Society》1999,127(5):1483-1491
We consider composition operators on Hardy spaces of a half-plane. We mainly study boundedness and compactness. We prove that on these spaces there are no compact composition operators.
18.
罗罗 《数学年刊A辑(中文版)》2017,38(3):265-268
作者证明了复合算子C_φ是单位球上加权Begrman空间上的保范算子当且仅当φ是旋转变换.对单位球上的Hardy空间上的保范复合算子仅得到部分结果. 相似文献
19.
20.
In this paper, we study composition operators on a Banach space of analytic functions, denoted byX, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman spaceL
α
1
(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those
which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
Supported by NNSFC No.19671036 相似文献