共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
We describe a general method to construct completely bounded idempotent mappings on operator spaces, starting from amenable
semigroups of completely bounded mappings. We then explore several applications of that method to injective operator spaces,
fixed points of completely contractive mappings, Toeplitz operators, dynamical systems and similarity orbits of group representations. 相似文献
3.
4.
Satoshi Yamaji 《Complex Analysis and Operator Theory》2014,8(4):863-873
We give estimates for the essential norm of a bounded little Hankel operator with $L^2$ symbol on weighted Bergman spaces of the unit ball in terms of a certain integral transform of the symbol. As an application of these estimates, we also give a necessary and sufficient condition for the little Hankel operators to be compact. 相似文献
5.
Trieu Le 《Integral Equations and Operator Theory》2010,67(3):425-438
Let ${\vartheta}$ be a measure on the polydisc ${\mathbb{D}^n}$ which is the product of n regular Borel probability measures so that ${\vartheta([r,1)^n\times\mathbb{T}^n) >0 }$ for all 0 < r < 1. The Bergman space ${A^2_{\vartheta}}$ consists of all holomorphic functions that are square integrable with respect to ${\vartheta}$ . In one dimension, it is well known that if f is continuous on the closed disc ${\overline{\mathbb{D}}}$ , then the Hankel operator H f is compact on ${A^2_\vartheta}$ . In this paper we show that for n ≥ 2 and f a continuous function on ${{\overline{\mathbb{D}}}^n}$ , H f is compact on ${A^2_\vartheta}$ if and only if there is a decomposition f = h + g, where h belongs to ${A^2_\vartheta}$ and ${\lim_{z\to\partial\mathbb{D}^n}g(z)=0}$ . 相似文献
6.
Benoit Florent Sehba 《Integral Equations and Operator Theory》2008,62(2):233-245
We present here some criteria for Schatten-Von Neumann class membership for the small Hankel operator on Bergman space A
2(T
Ω), when T
Ω is the tube over the symmetric cone Ω.
The author would like to thank professor Aline Bonami for helpful advices. 相似文献
7.
刘永民 《数学物理学报(A辑)》2004,24(3):375-380
讨论了 C\+n 中有界对称域的加权Bergman空间上符号属于 L\+2\-a(Ω, dV\-λ) 的小Hankel算子, 利用符号 Φ 的某种积分变换,给出了小Hankel算子 h\-Φ 属于Schatten理想 S\-p 的特征. 相似文献
8.
This paper is devoted to studying Bergman spaces A_(ω_(1,2)) ~p(M)(1 p ∞) induced by regular-weight ω_(1,2) on annulus M.We characterize the function f in L_(ω_(1,2)) ~1(M) for which the induced Hankel operator H_f is bounded(or compact) from A_(ω_(1,2))~p(M) to L_(ω_(1,2)) ~q(M) with 1 p,q ∞. 相似文献
9.
高进寿 《数学物理学报(A辑)》2000,20(1):41-47
在文中,对于C^m中有界强拟凸域Ω,得到了Bergman空间A^2(Ω)上的Hankel算子Hf(f∈L^2(Ω,dv)的本性范数∥Hf∥ess(在L^2(Ω,dv上)的等价刻划。 相似文献
10.
Compact Operators on Bergman Spaces 总被引:2,自引:0,他引:2
We prove that a bounded operator S on L
a
p
for p > 1 is compact if
and only if the Berezin transform of S vanishes on the boundary of the unit
disk if S satisfies some integrable conditions. Some estimates about the norm
and essential norm of Toeplitz operators with symbols in BT are obtained. 相似文献
11.
12.
证明了Bergman空间上的两个小Hankel算子如果是可交换的且其中一个是拟齐次的小Hankel算子,则另一个也是拟齐次的.还研究了Toeplitz算子和小Hankel算子的交换性. 相似文献
13.
S. Asserda 《Integral Equations and Operator Theory》2006,55(1):1-18
Let
denote the closed subspace of
consisting of analytic functions in the unit disc
. For certain class of subharmonic functions
and
, it is shown that the essential norm of Hankel operator
is comparable to the distance norm from Hf to compact Hankel operators. 相似文献
14.
We consider the weighted Bergman spaces
HL2(\mathbb Bd, ml){\mathcal {H}L^{2}(\mathbb {B}^{d}, \mu_{\lambda})}, where we set dml(z) = cl(1-|z|2)l dt(z){d\mu_{\lambda}(z) = c_{\lambda}(1-|z|^2)^{\lambda} d\tau(z)}, with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators
on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which
the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert–Schmidt operators on the generalized
Bergman spaces. 相似文献
15.
Bergman空间和q-Bloch空间之间的复合算子 总被引:4,自引:0,他引:4
本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子C(ψ)的有界性和紧性特征,得到了以下结论(1)C(ψ)是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件;(2)C(ψ)是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件;(3)C(ψ)是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子C0的范数估计,此处C0(f)(z)=fo(ψ)(z)-f((ψ)(0)). 相似文献
16.
本文讨论了Bergman空间和q-Bloch空间(小q-Bloch空间)之间的复合算子Cφ的有界性和紧性特征,得到了以下结论:(1)Cφ是q-Bloch空间(小q-Bloch空间)到Bergman空间的有界算子或紧算子之充要条件; (2)Cφ是Bergman空间到q-Bloch空间的有界算子或紧算子之充要条件; (3)Cφ是Bergman空间到小q-Bloch空间的有界算子或紧算子之充要条件,还给出了算子 Cφ0的范数估计,此处Cφ0(f)(z)=foφ(z)-f(φ(0)). 相似文献
17.
For 1 ≤ p ∞ we introduce a notion of “p-mean oscillation” on Cnin terms of the metric induced by reproducing kernel of F_Ψ~2. It is shown that the densely-defined Hankel operators ■ are simultaneously bounded if and only if f is of bounded “p-mean oscillation”.Furthermore, it is also shown that the densely-defined Hankel operators ■ are simultaneously compact if and only if f is of vanishing “p-mean oscillation”. Here the weight Ψ is a positive function of logarithmic growth satisfying certain suitable conditions. 相似文献
18.
Fengying Li 《Integral Equations and Operator Theory》2013,75(4):517-525
In this paper, we show that on the weighted Bergman space of the unit disk the essential norm of a noncompact Hankel operator equals its distance to the set of compact Hankel operators and is realized by infinitely many compact Hankel operators, which is analogous to the theorem of Axler, Berg, Jewell and Shields on the Hardy space in Axler et al. (Ann Math 109:601–612, 1979); moreover, the distance is realized by infinitely many compact Hankel operators with symbols continuous on the closure of the unit disk and vanishing on the unit circle. 相似文献
19.
Weighted Composition Operators on Bergman and Dirichlet Spaces 总被引:3,自引:0,他引:3
Let H() denote a functional Hilbert space of analytic functions on a domain . Let w : C and : be such that w f is in H() for every f in H(). The operator wC
given by f w f is called a weighted composition operator on H(). In this paper we characterize such operators and those for which (wC
)* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces. 相似文献
20.
首先证明广义Bergman空间A_(N,α)~p,(α-n-1,p0)上的复合算子C_φ的有界性和紧性是不依赖于p的,进而证明了若对某个q0和-n-1βα,C_φ在A_(N,β)~α上有界,则C_φ在A_(N,α)~p,α(α-n-1,p0)上是紧的当且仅当lim|z|→1-1-(|z|~2/1-|φ(1)|~2)=0. 相似文献